' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL] X  ` 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^Lõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- ( { Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(` d ֠z# u`:"COPYRIGHT 1982 BY DYNACOMP, INC."5 dD17000:DP n:15:6:"DISKETTE I"{ x6:12:"PLEASE WAIT A FEW SECONDS..." "RUN PART.1" 6,0:::470 z#?     ϠԮ#ԮԮԮ.Ԯ4!Ԯ   HELLO PROGRAM DISKETTE IC TOM HAMEL AND ERNIE WOODWARDX COPYRIGHT 1982q( APPLE II PLUS, 48K2:14:4:"PROBABILITY"<19:6:"BY"F5:9:"T. R. HAMEL AND E. L. WOODWARD"P6:12:"AUSTIN PEAY STATE UNIVERSITY"$ Z4:16BE ASKING YOU"bB"SOME QUESTIONS. YOU WILL ANSWER THESE QUESTIONS BY TYPING YOUR RESPONSE TO"L"ME. FROM YOUR ANSWERS I WILL BE ABLE TO FIND OUT HOW YOU ARE DOING AND"V"THEN PLAN LESSONS JUST FOR YOU. EACH TIME YOU TYPE A RESPONSE TO ME WILL BE LEARNING"h$"ABOUT PROBABILITY, ONE OF THE MOST INTERESTING AND PRACTICAL BRANCHES OF "."MATHEMATICS. TO DO THIS I WILL PRESENT YOU MESSAGES LIKE THIS ONE. OCCASION-"8"ALLY I WILL SHOW YOU A PICTURE ON THE SCREEN. I WILL ALSO OF PROGRAM +14:6:"PROBABILITY"A17:10:"PART I"]14:14:"INTRODUCTION"I929:I:3:"#":I:20:"#":I J419:9:J:"#";:29:"#":J I17000:I"HELLO. WELCOME TO THIS SPECIAL MATHE- MATICS PROGRAM. YOU I1L'(B$,I,1)"/"LMI:6803LMI:IBLM1ī800QLMLī800k((B$,LLM))0ī800}(B$)0ī8001300 " YOU HAVE ENTERED AN INVALID FRACTION. PLEASE TRY AGAIN."*B$:630 PROBABILITY  INTRODUCTORY PART CONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."h+N508,508,508,508,508,508,560,565,570,575,580,585{0"RUN PART.7"5"RUN PART.8":"RUN PART.9"?"RUN PART.10"D"RUN PART.11"I"RUN PART.12"XB$vL(B$)L3ī800N510,515,520,525,530,5351"RUN PART.1"D"RUN PART.2"W"RUN PART.3"j "RUN PART.4"}"RUN PART.5""RUN PART.6"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."'553(B$1):" PLEASE WAIT A FEW SETHE PROGRAM. IN THE EVENT THAT""YOU WANT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484::" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."GRAM."x:" WOULD YOU LIKE TO WORK ON ANOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND""PRESS ";::"RETURN";::".";480B$(B$,1)"Y"ė:400:" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF N:N1000,504,504,504,504,504,550,550,550,550,550,550x:"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400:" YOU HAVE JUST COMPLETED PART ";N;". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROYING CARDS":" 8. NUMBER CARDS":" 9. MARBLE BAG-COMPLEX"z " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 4607 LISTED HERE SO THAT YOU MAY DO ONE OR"w h"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE"= " 6. COINS":" 7. PLA,LM1)) LML1DEN1:3004 "DEN((B$,LLM))A ,DEN0KQ 1ANSNUMDENW 6] @{ J *LIST OF PROGRAM PARTS* T:" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH"' ^"THESE PARTS IN ORDER. THE PARTS ARE NO AND THEN PRESS THE RETURN KEY."2 ::1000: B$P (B$,1)"N"ī340Z 1000 **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS** L(B$) K I1L (B$,I,1)"/"ī270 I LMI L0īK NUM((B$EPARED BY"N 13:10:"E. L. WOODWARD":18:12:"AND":14:14:"T. R. HAMEL"t I929:I:3:"#":I:20:"#":I J419:9:J:"#";:29:"#":J I17000:I# :1:5:" IS THIS THE FIRST TIME FOR YOU TO WORKWITH THIS PROGRAM? ANSWER YES OR!2 *PART.1*<N1+FA$(10),B$(10)=d PROBABILITYCn]x14:6:"PROBABILITY"t16:10:"THROUGH"12:14:"PROBLEM SOLVING"I929:I:3:"#":I:20:"#":IJ419:9:J:"#";:29:"#":JI17000:I :14:6:"PR           A PRETTY GOOD WAY TO THINK ABOUT IT. I PREDICT"&"THAT THE WEATHERMAN USES THE WORD CHANCE MORE THAN ANYONE WITH WHOM YOU HAVE REGULAR CONTACT. ";A$;","&"IT IS COMMON FOR THE WEATHERMAN TO SAY THE CHANCE OF RAIN TODAY IS 40%."'"WALSO, LOOK AT THE LOWER-LEFT OF THE SCREEN AND DO AS WE PRACTICED EARLIER."j%2:22::"RETURN";:u%1715}%B$%216,0:%" NOW LET'S INVESTIGATE PROBABILITY. MOST PEOPLE USE THE WORD PROBABILITY"3&"TO MEAN CHANCE AND THAT IS ESS ";::"RETURN";:$r" OR I WILL JUST WAIT":"ON YOU FOREVER. LET'S SEE IF YOU UNDER- STAND. TELL ME YOUR FAVORITE COLOR.":$1680$B$$:" YOU JUST TOLD ME THAT YOUR FAVORITE COLOR IS ";B$;"."P%:"I AM READY TO GO ON. IF YOU ARE TRY THIS RIGHT NOW.":2:20::"RETURN";:5#J1620=#OB$J#T216,0:#^:" THERE IS JUST ONE MORE THING WE NEED TO DISCUSS. MANY TIMES I WILL ASK YOU A"$h"QUESTION. WHENEVER YOU SEE THE '?' ON THE SCREEN YOU MUST GIVE ME SOME ANSWER AND PR FEW MORE THINGS WE NEED TO TALK ABOUT NOW. ANYTIME I PUT"",:"RETURN";::" IN THE LOWER-LEFT CORNER OF THE":"SCREEN IT MEANS YOU ARE TO PRESS THE""6:"RETURN";::" KEY WHEN YOU ARE FINISHED LOOK-":"ING AT WHAT IS ON THE SCREEN. LET'S"*#@"CTICE ANOTHER CORREC- TION? ANSWER ";::"Y OR N AND RETURN":I!1540Q!B$h!(B$,1)"N"ī1560!:"PRACTICE ANOTHER CORRECTION BUT DON'T FORGET TO PRESS ";::"RETURN";::" WHEN YOU ARE FINISHED.":1510!216,0:<""" THERE ARE A"ING 80. PRACTICE THIS EXAMPLE(OR ONE":"OF YOUR OWN) USING THE ";::"LEFT ARROW": "KEY. DON'T FORGET TO PRESS ";::"RETURN";::" WHEN":"YOU ARE HAPPY WITH YOUR ANSWER." 1520 B$>!"YOU GAVE ME THE ANSWER ";B$:"DO YOU WANT TO PRALAD YOU ARE READY TO CONTINUE":A$;". YOU MAY NEED TO PRACTICE""USING THE ";::"LEFT ARROW";::" KEY. SUPPOSE":"YOU TYPED 5270 BUT MEANT TO TYPE 5280.""YOU COULD CORRECT THIS BY PRESSING THE"::"LEFT ARROW";::" KEY TWICE AND THEN TYP-"W ME CORRECTLY. DID YOU TELL ME YOUR NAME"}"CORRECTLY? ANSWER ";::"Y";::" OR ";::"N";::" AND ";::"RETURN":1430B$1440(B$,1)"Y"ī1450:"OK, I WILL GIVE YOU ANOTHER CHANCE.":1360216,0:?" I'M GUR FRACTION IS ";B$:1300&<216,0:P" SO I KNOW WHO I AM TEACHING, TYPE YOUR FIRST NAME AND PRESS ";::"RETURN";::"."U1390ZA$d STUDENT'S NAME IS IN A$nA$;", I AM GLAD TO MEET YOU."-x"I HOPE YOU TOLD ME YOUR FIRST NA GOOD! WOULD YOU LIKE TO PRACTICE MAKING MORE FRACTIONS? IF SO TYPE":"Y";::" AND ";::"RETURN";::", IF NOT TYPE ";::"N";::" AND ";::"RETURN";:1320B$:(B$,1)"N"ī1340#1330("ENTER A FRACTION: ";:B$2"YO PRESS THE ";::"RETURN";::" KEY. I WOULD LIKE FOR YOU""TO PRACTICE MAKING A FEW FRACTIONS AND I WILL PRINT THEM BACK OUT TO YOU."216,01290"ENTER A FRACTION:";:B$30:23:B$; I1500:I216,0:630J""MAKE A MISTAKE AND DISCOVER IT BEFORE""YOU PRESS THE ";::"RETURN";::" KEY YOU CAN":"ERASE YOUR ANSWER BY PRESSING THE":"LEFT ARROW";::" KEY AS MANY TIMES AS":"IS NEEDED TO ERASE YOUR ANSWER. THEN"<"ENTER YOUR CORRECTED ANSWER AND 3/4 5/8 12/25 7/3":p" ALL YOU NEED TO DO IS TO TYPE THE TOP NUMBER, TYPE THE SLASH(THE KEY""WITH THE ? AND / ON IT), AND THEN THE BOTTOM NUMBER. WHEN YOU ARE DONE YOU"'"PRESS THE ";::"RETURN";::" KEY. IF YOU SHOULD ":216,0:Y" EXCELLENT! MANY TIMES I WILL ASK YOU QUESTIONS IN WHICH YOUR ANSWER""WILL BE A FRACTION. YOU MUST LEARN TO TYPE FRACTIONS. TO DO THIS YOU""JUST TYPE THE FRACTION AS IT LOOKS IN THE FOLLOWING EXAMPLES:"" YOU"f`"MUST CONCLUDE YOUR MESSAGE TO ME BY PRESSING THE ";::"RETURN";::" KEY. THIS WAY I"j"KNOW YOU HAVE FINISHED.":t:"RETURN";::" THAT IS, PRESS THE RETURN":"KEY WHEN YOU ARE READY TO GO ON."y216,0|1155~B$B$ ):470 N BITY OF RAIN IS 2/5. AS A MATTER OF FACT, THE PROBABILITY OF"("SOME EVENT OCCURRING IS A NUMBER AND IN THIS LESSON OUR PROBABILITIES WILL BE GIVEN IN FRACTIONAL FORM, NOT PERCENTAGE FORM."(&2:22::"RETURN";:(+N1(0470)5HEN HE SAYS THIS THE WEATHERMAN MEANS THAT IF THERE WERE 100 DAYS WITH CON- DITIONS EXACTLY LIKE THOSE EXISTING WHEN HE MADE HIS PREDICTION, IT WOULD"?("RAIN ON 40 OF THOSE DAYS. HOWEVER, SINCE 40% = 40/100 = 2/5, I WOULD SAY THE PROBABIL` 2430 j ANSWER IS CORRECTot "YOUR ANSWER OF ";B$;" IS CORRECT SINCE":"2 OF THE 7 MARBLES ARE WHITE."~ 2:23::"RETURN";: 2450 B$ K2:2100 3:2:"SUPPOSE ALL 7 MARBLES ARE" "PUT BACK IN THE BAG AND" "THAT YOU AND ";::"RETURN";::". ";:K2380,K6B$:GB$""ī2380WK2370:230j8 ANS27ī2410t= 2380B : ANSWER INCORRECTL "YOUR ANSWER OF ";B$;" IS NOT CORRECT SINCE":"2 OF THE 7 MARBLES ARE WHITE THE COR- RECT ANSWER IS 2/7."MARBLE WAS SELECTED IS 4/7. NOW HERE IS A QUESTION FOR YOU."C" SUPPOSE ALL 7 MARBLES ARE PUT BACK IN THE BAG AND THAT YOU DRAW A MARBLE""WITHOUT LOOKING. WHAT IS THE PROBABIL- ITY THAT YOU DRAW A WHITE MARBLE?"$"INPUT A FRACTIONND 1 OF"+"WHICH IS BLUE. SUPPOSE THAT"L"YOU REACHED INTO THIS BAG"o"WITHOUT LOOKING AND REMOVED""ONE MARBLE. SINCE THERE ARE""EXACTLY 4 RED MARBLES AND EXACTLY 7 MARBLES ALTOGETHER, WE SAY THE PROB-"="ABILITY THAT A RED #"A33:4:"# #"/B33:5:"#W R W#"EC33:6:"# #"[D33:7:"#R B R#"qE33:8:"#######"RK2ī2455f3:2:"NOW WE WILL CONSIDER THE"p"CASE OF A BAG OF MARBLES,"z"4 OF WHICH ARE RED, 2 OF""WHICH ARE WHITE, APROBABILITY""17:10:"PART 2"B12:14:"MARBLES IN A BAG"hI929:I:3:"#":I:20:"#":IJ419:9:J:"#";:29:"#":JI17000:I K14 *BAG OF MARBLES,4R,2W,1B*9>35:1:"# #"?35:2:"# #"@34:3:"# RM THE DISK."C.N500,500,500,500,500,500,560,565,570,575,580,585V0"RUN PART.7"i5"RUN PART.8"|:"RUN PART.9"?"RUN PART.10"D"RUN PART.11"I"RUN PART.12" *PROBABILITY* *PART 2,MARBLES IN A BAG* 14:6:"RUN PART.1""RUN PART.2"2"RUN PART.3"E "RUN PART.4"X"RUN PART.5"k"RUN PART.6"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."(554)B$ *:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FRONT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484::" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."N510,2000,520,525,530,535 "NOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"p "PRESS ";::"RETURN";::".";z 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"x"YOU WA550,550,550L :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."L :" WOULD YOU LIKE TO WORK ON ARBLE BAG-COMPLEX"N " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N504,2000,504,504,504,504,550,550,550,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MA$,LLM)) ,DEN0K% 1ANSNUMDEN+ 61 @O J *LIST OF PROGRAM PARTS* T:" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT YOU MAY DO ONE OR"K h2 *PART.2*<N2$FB$(10).Z2000r **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**~L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((B          B$ #D 470 I::"RETURN";:+#5 31403#: B$<#D 470 PROBABILITY THAT THE MARBLE DRAWN IS BLUE";7" K3100?" KG" B$X" B$""ī3100h" K3096:230|" ANS211ī3110" 3100" " :"SORRY, THE CORRECT ANSWER IS 2/11.":3120"& :"THAT'S RIGHT!!""0 2:22::"RETURN";:"5 3140#: NDOM. WHAT IS THE":"PROBABILITY THAT THE MARBLE":"SELECTED IS WHITE";R! 3020Z! B$k! B$""ī3040{! K3035:230! ANS411ī3050! 3040! ! :"SORRY, THE CORRECT ANSWER IS 4/11.":3060! :"YOU ARE CORRECT!!"," :"WHAT IS THEER IS CORRECT.") t 2:22::"RETURN";:4 v 2940< x B$I | 216,0:f 2780: *BAG OF MARBLES* 1:2:" AGAIN CONSIDER THE BAG WHICH":"CONTAINS 5 RED, 4 WHITE, AND":"2 BLUE MARBLES. SUPPOSE ONE"G! "MARBLE IS SELECTED FROM THE":"BAG AT RA K2875:230 6 ANS511ī2920*8 28800; @ :"SORRY, YOUR ANSWER IS NOT":"CORRECT. SINCE THE BAG CONTAINS ELEVEN MARBLES ALTOGETHER AND SINCE THERE"T "ARE 5 RED MARBLES THE CORRECT ANSWER IS 5/11."^ 2932 h :"VERY GOOD, YOUR ANSW RED, 4 WHITE, AND":"2 BLUE MARBLES. SUPPOSE ONE" "MARBLE IS SELECTED FROM THE":"BAG AT RANDOM. WHAT IS THE":"PROBABILITY THAT THE MARBLE":"SELECTED IS RED?": :"INPUT A FRACTION AND RETURN";: K2880" K' B$) B$""ī2880 ,W,2B*   32:1:"* *"3 32:2:"* *"I 31:3:"* R *"a 30:4:"* R W *"y 30:5:"* R R R *" 30:6:"* W B *" 30:7:"* W B W *" 30:8:"*********" 2 1:2:" NEXT WE CONSIDER A BAG WHICH":"CONTAINS 5OBLEM WE FOUND THAT THERE WERE 4 RED MARBLES OUT OF A TOTAL OF 7 MARBLES" "WHICH MEANT THAT THE PROBABILITY OF DRAWING A RED MARBLE WAS 4/7." 2:23::"RETURN";: 2750 B$ 216,0: 2780 2810 *BAG OF MARBLES 5R,4R. IN SUCH A CASE THE PROBABILITY THAT AN EVENT OCCURS IS:"t :" THE NUMBER OF WAYS THE EVENT CAN OCCUR" " --------------------------------------" " THE TOTAL NUMBER OF OUTCOMES"J :" AGAIN RETURNING TO THE MARBLE BAG PR"IT IS EASY TO IDENTIFY"WP "A NUMBER OF EQUALLY LIKELY":"OUTCOMES. FOR EXAMPLE, IN"Z "THE CASE OF THE MARBLE BAG":"THAT WE JUST INVESTIGATED,"d "THERE WERE 7 MARBLES IN THE":"BAG AND EACH MARBLE WAS AS"Cn "LIKELY TO BE SELECTED AS ANY OTHEG OF MARBLES 4R,2W,1B*- 02 32:1:"* *"D3 32:2:"* *"Z4 31:3:"* R *"r5 30:4:"* *"6 30:5:"* R R R *"7 30:6:"* *"8 30:7:"* W B W *"9 30:8:"*********"F 1:2:" IN MANY PROBABILITY PROBLEMS":p "YOUR ANSWER OF ";B$;" IS NOT CORRECT.":"SINCE 1 OF THE 7 MARBLES IS BLUE THE CORRECT ANSWER IS 1/7."z 2570 :"YOUR ANSWER OF ";B$;" IS CORRECT SINCE":"1 OF THE 7 MARBLES IS BLUE." 2:23::"RETURN";: 2605 B$( *BADRAW A MARBLE". "WITHOUT LOOKING. WHAT IS"N "THE PROBABILITY THAT YOU"k "DRAW THE BLUE MARBLE?"q  "INPUT A FRACTION AND ";::"RETURN";::".";  2500 B$ B$""ī2520 K2515:230 ANS17ī2550 2520 THE CORRECT ANSWER IS 1/4.":3590F:" YOUR ANSWER IS CORRECT."[::"RETURN";:f3600n B$3700:3800:3860:3910" WHAT IS THE PROBABILITY THAT THE ARROW WILL POINT TO 'A'";3647$B$)B$""ī3647 . SEE THE SMALLER REGIONS.";/ :"RETURN";:: 3540B B$L 3860R  "NOW WHAT IS THE PROBABILITY THAT THE SPINNER WILL POINT TO 'A'"; 3570 B$ B$""ī3579 K3578:230 ANS14ī3585 3579  # "W WILL POINT TO THE'A' RE- GION IS NOT 1/2 SINCE THE REGIONS ARE OF DIFFERENT SIZE.";j :"RETURN";:u 3498} B$  "IF WE SEPARATE THE 'C' REGION INTO 3 SMALLER REGIONS IT WILL BE EASIER TO FIND THE PROBABILITY. PRESS RETURN TO IS 1/2.";:3460f p " YES. SINCE THERE ARE 2 REGIONS OF THE SAME SIZE THE ARROW IS EQUALLY LIKELY TO POINT TO EITHER REGION." :"RETURN";: 3480 B$ 3700:3800 W "FOR THE SPINNER ABOVE THE PROBABILITY THAT THE ARRO WOULD POINT TO THE 'A' REGION";,* 339044 B$E9 B$""ī3403U> K3402:230hH ANS12ī3430rI 3403xJ ~K M " NO. SINCE THERE ARE 2 REGIONS EXACTLY THE SAME SIZE, THE ARROW IS AS LIKELY TO POINT TO EITHER REGION. THUS THE ANS-WERART 3" 16:14:"SPINNERS"D I929:I:3:"#":I:20:"#":Ih J419:9:J:"#";:29:"#":Jy I17000:I 3700! " LOOK AT THE SPINNER PICTURED ABOVE. SUPPOSE YOU WERE ABLE TO SPIN THE ARROW.WHAT IS THE PROBABILITY THAT THE ARROWM THE DISK."C.N500,500,500,500,500,500,560,565,570,575,580,585V0"RUN PART.7"i5"RUN PART.8"|:"RUN PART.9"?"RUN PART.10"D"RUN PART.11"I"RUN PART.12" *PART 3,SPINNERS*  14:6:"PROBABILITY" 17:10:"PRUN PART.1""RUN PART.2"2"RUN PART.3"E "RUN PART.4"X"RUN PART.5"k"RUN PART.6"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."(554)B$ *:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FRONT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484::" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."N510,515,3300,525,530,535 "NOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"p "PRESS ";::"RETURN";::".";z 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"x"YOU WA550,550,550L :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."L :" WOULD YOU LIKE TO WORK ON ARBLE BAG-COMPLEX"N " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N504,504,3300,504,504,504,550,550,550,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MA$,LLM)) ,DEN0K% 1ANSNUMDEN+ 61 @O J *LIST OF PROGRAM PARTS* T:" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT YOU MAY DO ONE OR"K h2 *PART.3*<N3$FB$(10).Z3300r **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**~L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((B          AS A MATTER OF FACT ANYTIME THE PROB- ABILITY IS 0 WE ARE INDICATING THAT THIS EVENT CANNOT HAPPEN."s4295:"RETURN";:B$::470 B +|:" THE CORRECT ANSWER IS 0.":4240M:" GOOD! YOU ARE CORRECT."^I11000:Id:" NOTICE THAT IT IS NOT POSSIBLE FOR THEARROW TO POINT TO 'B' SINCE THERE IS NO 'B' REGION.":"RETURN";:4258B$h:" NS, THE PROBABILITY IS 3/8.":41508,:" CORRECT!"K6:"RETURN";:V;4170^@B$dJT" WHAT IS THE PROBABILITY THAT THE ARROW WILL POINT TO 'B'";Y4220^B$cB$""ī4220hK4215:230rANS0ī4230t4220wURN";:4080B$ b" WHAT IS THE PROBABILITY THAT THE ARROWWILL POINT TO 'C'";m4127uB$ B$""ī4127K4125:230ANS38ī41404127$"" SINCE THERE ARE 3 'C' REGIONS OUT OF A TOTAL OF 8 REGIO:33,22 Q:" WHAT IS THE PROBABILITY THAT THE ARROWWILL POINT TO 'O'";\4040dB$uB$""ī4040K4035:230ANS18ī40504040:" THE CORRECT ANSWER IS 1/8.":4060:" YES, THAT'S RIGHT."::"RETR D* K15,PI032:4I,I:4I,32I:IKU0:23,2411:12,1325:15aWJ1731:20,J:JwXI2135:I,16:IZ10,146:10,148:7,10:7,12d18,226:18,228:7,18:7,20n10,1432:10,1434:33,10:33,12x18,2232:18,2234:33,1817,3120:15:4,2016. *SPINNER C*U15:J18302:I150:I:20,J:Jx#I22342:J150:J:I,16:I(26,3022:26,3023:26,3024:0:27,2923:24,28:15226,3016:26,3017:26,3018:0:27,2917:18,28:15<F *SPINNE$ `4000t *SPINNER A*'y:15E~0,324:0,3236:0,3220Z4,360:4,3632z2,616:2,618:17,2:17,42,622:2,623:2,624I19:16I,20I:I23,2511:11,13250:3,523:24,4:15 *SPINNER B*0:K3645:2308ANS48ī3660):3647/=5?B" YOUR ANSWER IS WRONG. THE CORRECT ANSWER IS 4/8 SINCE THERE ARE 8 REGIONS AND 4 OF THESE ARE 'A'."G3665L:" YOUR ANSWER OF ";B$;" IS CORRECT."Q:"RETURN";:V4000[BI,16I:4I,16I:I9z14,1814:14,1816:15,14:15,16VI12288:I,1:I,31:IrJ8248:5,J:35,J:J12,16:20,16:" WHAT IS THE PROBABILITY THAT HE FALLS IN REGION A.";:K4800KB$B$""ī4800K4795:230B$""ī4660 K4655:230/*ANS316ī46709,4660?/d4:" THE ANSWER IS 3/16.":4680{>:" VERY GOOD!!"H:"RETURN";:J4690MB$R:15\4,360:4,3632:12,288:12,2824f0,324:0,3236:8,2428pI18:4 SMALLERRECTANGLES. THE 16 SMALLER RECTANGLES ARE ALL THE SAME SIZE. ";::"RETURN";:f4603nB$:" REGION A IS 'MADE UP' OF 3 OF THESE RECTANGLES. TRY AGAIN. WHAT IS THE PROB-ABILITY THAT HE FALLS IN REGION A";K B$ N";:4550B$W:" WHAT IS THE PROBABILITY THAT HE FALLS IN REGION A.";b4600jB${B$""ī4600K4595:230ANS316ī46704600[:" LOOK AT THE LARGE RECTANGLE. THIS LARGE RECTANGLE IS MADE UP OF 16I12288:I,1:I,31:I3J8248:5,J:35,J:JY!18,2223:18,2225:24,18:24,20:" SUPPOSE THAT THE LARGE RECTANGLE PIC- TURED ABOVE IS A MAP AND THAT A PARA- CHUTIST FALLS AT RANDOM ONTO THIS LARGE RECTANGLE.";30:24:"RETURRT 4" 14:15:"PARACHUTIST"FI929:I:3:"#":I:20:"#":IjJ419:9:J:"#";:29:"#":J{I17000:I:154,360:4,363220,288:12,2016:12,28240,324:0,3236 16,2412:8,1620:8,242812,8M THE DISK."C.N500,500,500,500,500,500,560,565,570,575,580,585V0"RUN PART.7"i5"RUN PART.8"|:"RUN PART.9"?"RUN PART.10"D"RUN PART.11"I"RUN PART.12" *PART 4,PARACHUTIST*:14:6:"PROBABILITY"17:10:"PARUN PART.1""RUN PART.2"2"RUN PART.3"E "RUN PART.4"X"RUN PART.5"k"RUN PART.6"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."(554)B$ *:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FRONT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484::" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."N510,515,520,4300,530,535 "NOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"p "PRESS ";::"RETURN";::".";z 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"x"YOU WA550,550,550L :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."L :" WOULD YOU LIKE TO WORK ON ARBLE BAG-COMPLEX"N " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N504,504,504,4300,504,504,550,550,550,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MA$,LLM)) ,DEN0K% 1ANSNUMDEN+ 61 @O J *LIST OF PROGRAM PARTS* T:" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT YOU MAY DO ONE OR"K h+2 *PART.4*<N4$FB$(10).Z4300r **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**~L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((B               230&ANS1316ī5660#&5610)&&:" SORRY, YOUR ANSWER IS WRONG. LOOK AT THE FIGURE AGAIN. COUNT THE SMALL REC- TANGLES THAT ARE IN AT LEAST ONE OF THESE TWO REGIONS. ";:K560&:"RETURN";:&K&B$J':" TRY AGAIN. HENCE THE CORRECT ANS- WER IS 3/16.":5550Y%:" YOUR ANSWER IS CORRECT. VERY GOOD."l%:"RETURN";:w%5570%B$%:" WHAT IS THE PROBABILITY THAT HE FALLS IN REGION A OR REGION C";:K5610%5610%B$%B$""ī5610&K5605:,20:15g$r:" WHAT IS THE PROBABILITY THAT THE PARA-CHUTIST FALLS IN REGION A AND REGION C?":K5530r$w5530z$|B$$B$""ī5525$K5530:230$ANS316ī5540$5530$+%:" NO. NOTICE THAT THERE ARE 3 RECTANGLESIN BOTH REGIONS.:20,3616:4,36322#,0,324:0,1620:16,3236O#6I12282:I,8:I,24:Il#@J8242:12,J:28,J:J#J12,1:35,24:I12288:I,31:I#OJ8248:5,J:J#T26,307:26,309:8,26:8,28#^18,2215:18,2217:18,2216$h0:19,2116:17 ANSWER IS NOT CORRECT. THERE ARE 14 RECTANGLES WHICH ARE IN AT LEAST ONE OF THESE TWO REGIONS. THE CORRECT ANSWERIS 14/16. ";:5380":" YES. WELL DONE."":"RETURN";:"5390"B$":15"I4368:J0328:I,J:J:I#"4,200L THERECTANGLES IN A OR C.";/!:"RETURN";::!5310B!B$!:" NOW TRY AGAIN. WHAT IS THE PROBABILITYTHAT HE FALLS IN REGION A OR C";:K5350!5350!B$!B$""ī5350!K5345:230!ANS78ī5370!5350!":" YOURHUTIST FALLS IN REGION A OR REGION C?":K53008 5300@ B$Q B$""ī5300a K5295:230t ANS78ī5370~ 5300 !:" LOOK CAREFULLY AT THE PICTURE ABOVE. REMEMBER IN THIS SITUATION THE WORD 'OR'MEANS AT LEAST ONE REGION. COUNT AL5230\5220_d:" NO. SINCE THERE ARE 4 RECTANGLES THAT A AND C HAVE IN COMMON, THE CORRECT ANS-WER IS 4/16.":5235n:" CORRECT. THAT IS VERY GOOD."s:"RETURN";:x5250}B$- :" WHAT IS THE PROBABILITY THAT THE PARA-CK5175:2302ANS14ī5230)45180/7<:" REMEMBER THAT 'AND' IN THIS CASE MEANSBOTH REGIONS. AGAIN, WHAT IS THE PROB- ABILITY THAT HE FALLS IN REGION A AND REGION C";:K5220FKKB$MB$""ī5220PK5215:230ZANS14OUR ANSWER IS INCORRECT. THE CORRECT ANSWER IS 9/16.":5120V:" THAT'S CORRECT."i:"RETURN";:t5140| B$:" WHAT IS THE PROBABILITY THAT THE PARA-CHUTIST FALLS IN REGION A AND REGION C":K5180KB$#B$""ī5180 (:8,2:8,4,26,3031:26,3032:26,3033H0:27,2932:33,28:15:" WHAT IS THE PROBABILITY THAT THE PARACHUTIST FALLS IN REGION A";:K5100KB$B$""ī5100K5095:230ANS916ī51105100;:" Y"B2:22::"RETURN";:&L4970.VB$8j:15[tI4368:J0328:I,J:J:I~4,280:4,2824:0,244:0,242812,1:20,1:5,8:5,1623,2520:27,2916I12362:I,8:I,32:IJ8322:12,J:36,J:J 2,67:2,69HESE PROBLEMS";."INVOLVE THE WORDS 'AND' AND 'OR'. WHEN I SAY THE PARACHUTIST FALLS IN REGION A AND C I MEAN HE FALLS IN BOTH REGIONS.WHEN I SAY THE PARACHUTIST FALLS IN"8"REGION A OR C I MEAN HE FALLS IN AT LEAST ONE OF THESE TWO REGIONS. PROBLEMS ARE A LITTLE MORE COMPLEX AND THE PICTURES ARE QUITE HARD TO DRAW. FOR SIMPLICITY SAKE I"$"WILL NOT MAKE THE PICTURE OF THE LARGE RECTANGLE. IN EACH CASE IT WILL BE UN- DERSTOOD THAT THE PARACHUTIST FALLS INTOTHAT RECTANGLE AT RANDOM. TN REGION A";4850B$0B$""ī4850@K4845:230TANS516ī4860^4850d:" NO. THE CORRECT ANSWER IS 5/16.":4870:" THAT'S CORRECT. VERY GOOD!"::"RETURN";: 4880 B$:f" THE NEXT FEWANS516ī48604800:" NOTICE THAT REGION A CONTAINS 4 SMALL RECTANGLES AND 2 TRIANGLES WHICH ARE HALF AS BIG AS A SMALL RECTANGLE.":"RETURN";:4805B$ :" NOW TRY AGAIN. WHAT IS THE PROBABILITYTHAT HE FALLS IGION A. OF THESE 11 REC- TANGLES 4 ARE ALSO IN REGION C. THE COR-RECT ANSWER IS 4/11.";:63703:" YOUR ANSWER IS CORRECT."::3:"RETURN";:363803B$3216,0:::470 B KRECT."::3:"RETURN";:363803B$ 421 SUPPOSE THAT YOU KNOW THAT HE FALLS INREGION A. WHAT IS THE PROBABILITY THAT HE ALSO FALLS IN REGION C";u26350}2B$2B$""ī63502K6345:2302ANS411ī6360263502_3:" NOTICE THAT THERE ARE 11 SMALL REC- TANGLES IN REST ONE OF THE TWO REGIONS, THE COR- RECT ANSWER IS 16/16 OR 1.":6280\1~:" CORRECT.":o1:"RETURN";:z162901B$1:" IN GENERAL, A PROBABILITY OF 1 MEANS THAT AN EVENT MUST HAPPEN."1::"RETURN";:163001B$j2:" 31:2,632:2,633:0:3,532:33,4:15w0B:" WHAT IS THE PROBABILITY THAT HE WILL LAND IN REGION A OR REGION C";0L62600VB$0[B$""ī62600`K6255:2300jANS1ī62700l62600oF1t:" SINCE ALL 16 RECTANGLES ARE IN AT LEA248:5,J:J:I12288:I,31:I/11,138:11,1316:19,218:15,1728:23,2520:23,2528:28,1:35,8:12,31:20,31:28,31/20,1:35,16/I08:12I,I:28I,16I:I/I18:12I,I1:27I,16I:I/$26,307:26,309:8,26:8,28(0.2,6.:" CORRECT. VERY GOOD."4.::"RETURN";:?.6110G.B$Q.:15t.I4368:J0328:I,J:J:I.4,120:20,2816:4,3632:0,324:8,1620:24,3236.J0242:12,J:36,J:J:I12362:I,0:I,24:I!/I20362:I,0:I:J80 -B$L-:" WHAT IS THE PROBABILITY THAT HE FALLS OUTSIDE REGION A";W-6070_-B$p-B$""ī6070-K6065:230-ANS34ī6080-6070-.:" THERE ARE 12 RECTANGLES OUTSIDE REGIONA. THUS, THE CORRECT ANSWER IS 12/16.":6090ALLS IN REGION A AND REGION C";*,C59902,HB$C,MB$""ī5990S,RK5985:230d,\ANS0ī6000n,^5990t,a,f:" SINCE THERE ARE NO RECTANGLES IN BOTH REGIONS, THE CORRECT ANSWER IS 0.":6010,p:" CORRECT.",z::"RETURN";:-|60216:28,3624:20,2832Q+0,164:8,1612:0,828:16,3220:24,3228:16,2436z+5,8:12,1:20,1:20,7:28,17:21,24+2,67:2,69:8,2:8,4+18,2223:18,2224:18,2225+0:19,2124:25,20:15,>:" WHAT IS THE PROBABILITY THAT HE F5790*5780*q*:" THERE ARE 4 RECTANGLES OUTSIDE REGION A. HENCE THE CORRECT ANSWER IS 4/16.":5800*:" CORRECT.":*:"RETURN";:*5810*B$*:15*I4368:J0328:I,J:J:I+4,280:12,288:4,1216:20,36 RECTANGLES WHICH ARE OUTSIDE REGION A. NOW WHAT IS THE PROB- ABILITY THAT HE FALLS OUTSIDE REGION A?":K5780z)d5750)l:" THAT WAS A HARD QUESTION BUT YOUR ANS-WER IS CORRECT.":5800)vK){B$)}B$""ī5780)K5775:230*ANS14IS 13/16.":5670$(:" CORRECT."7(&:"RETURN";:B(+5690J(0B$(::" WHAT IS THE PROBABILITY THAT HE FALLS OUTSIDE REGION A";:K5730(?K(DB$(IB$""ī5730(NK5725:230(XANS14ī5740(Z5730(]p)b:" NO. COUNT THE WHAT IS THE PROBABILITY THAT HE FALLS IN REGION A OR REGION C?":K5650R'KZ'B$k'B$""ī5650{'K5645:230'ANS1316ī5660' 5650' (:" SINCE THERE ARE 13 RECTANGLES WHICH ARE IN REGION A OR REGION C, THE CORRECTANSWER E OF THESE SIDES IS A '5', THE PROBABILITY IS 1/6."M2:22::"RETURN";:X6690`B$~6700:*CLEAR BELOW DICE*"6720,I622:1:I:" ":I6J622:40:J:" ";:J:L@1:6:" LET'S TRY AE UP AS ANY OTHER SIDE"p"AND SINCE THE '5' CAN TURN UP IN ONLY ONE WAY, THE CORRECT ANSWER IS 1/6.":6660" YES, THAT'S CORRECT. THERE ARE SIX SIDES ON THE DIE AND EACH SIDE IS AS"3"LIKELY TO TURN UP AS ANY OTHER SIDE. SINCE ONLY ONTHIS DIE RANDOMLY. WHAT IS THE PROBABILITY THAT YOU GET A '5'";M6610UB$fB$""ī6610vK6605:230ANS16ī66406610" NO, YOUR ANSWER IS INCORRECT. SINCE THE DIE HAS SIX SIDES AND EACH SIDE IS AS LIKELY TO COM SIX-SIDED DIE. THE SIDES OF SUCH A DIE ARE PICTURED ABOVE."x" WHEN I TALK ABOUT A DIE I WILL WRITE '1' WHEN REFERRING TO THE SIDE WITH ONE #, '2' WHEN REFERRING TO THE SIDE WITH TWO #'S, AND SO ON FOR THE OTHER SIDES."B" SUPPOSE YOU TOSS :" ";:28:" # ";:34:" "iF4:" ";:10:" #";:16:" #";:22:"# #";:28:"# #";:34:"###"oKP5:"1";:11:"2";:17:"3";:23:"4";:29:"5";:35:"6"U?d1:6:" I AM SURE THAT SOMETIME IN YOUR LIFE YOU HAVE SEEN A STANDARD17:10:"PART 5"(18:15:"DICE"NI929:I:3:"#":I:20:"#":Ir J419:9:J:"#";:29:"#":J#I17000:I(:24:" ";:10:"# ";:16:"# ";:22:"# #";:28:"# #";:34:"###"<4:" # ";:10:" ";:16:" # ";:22";N:"TO BE LOADED FROM THE DISK."Y.N500,500,500,500,500,500,560,565,570,575,580,585l0"RUN PART.7"5"RUN PART.8":"RUN PART.9"?"RUN PART.10"D"RUN PART.11"I"RUN PART.12" *PART 5,DICE* :14:6:"PROBABILITY"20,525,6400,535""RUN PART.1"5"RUN PART.2"H"RUN PART.3"[ "RUN PART.4"n"RUN PART.5""RUN PART.6"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."(554)B$"*:" PLEASE WAIT A FEW SECONDS FOR PART ENT THAT""YOU WANT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484::" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."N510,515,5 YOU LIKE TO WORK ON ANOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND" "PRESS ";::"RETURN";::"."; 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EV,6400,504,550,550,550,550,550,550b :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."b :" WOULDMBER CARDS":" 9. MARBLE BAG-COMPLEX"d " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460! N:N504,504,504,504OU MAY DO ONE OR"a h"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE"' " 6. COINS":" 7. PLAYING CARDS":" 8. NUN1:300 "DEN((B$,LLM))+ ,DEN0K; 1ANSNUMDENA 6G @e J *LIST OF PROGRAM PARTS* T:" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT Y22 *PART.5*<N5$FB$(10):PMUS(12),RL(2,10)DZ6400 **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1)) LML1DE                  ":40:J:" ";:J:@&`:" YES."Z&j2:22::"RETURN";:e&l7540m&oB$u&qC0&t7500:1:10:" WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM OF 7";&y7580&~B$&B$""ī7580&K7575:230'ANS175008%.1:10:" WHICH SUM IS MOST LIKELY TO OCCUR";C%37495J%8DY%BD7ī7520%G:" NO. THE ANSWER IS 7 SINCE 7 OCCURS IN SIX DIFFERENT WAYS AND EVERY OTHER POS- SIBLE SUM OCCURS IN FEWER THAN SIX WAYS.":75300&LJ922:1:J:" E WAYS WE CAN GET A SUM OF 5."o$17:15:"R:G":17:16:"---":17:17:"4:1":17:18:"3:2":17:19:"2:3"$ 17:20:"1:4":" THUS THE CORRECT ANSWER IS 4.":7450$:" YOUR ANSWER IS CORRECT."$2:22::"RETURN";:$7460$B$%$RN UP 1. THUS, THE CORRECT ANSWER IS 1.":7370D#:" CORRECT."^#2:22::"RETURN";:i#7380q#B${#7500#1:10:" IN HOW MANY WAYS CAN YOU GET A SUM OF 5";#7420#D#D4ī7440 $" NO. HERE IS A TABLE WHICH SHOWS THNOW WHEN WE WORK WITH A PAIR OF DICE WE ARE USUALLY CONCERNED WITH THE SUM"""THAT WE GET FROM THE DICE. IN HOW MANY WAYS CAN WE GET A SUM OF 2";"7350"D"D1ī73600#:" NO. THE ONLY WAY YOU CAN GET A SUM OF 2 IS FOR EACH DIE TO TUICE THAT EVERY POSSIBLE OUTCOME IS LISTED EXACTLY ONCE. HOW MANY POSSIBLE OUTCOMES ARE THERE";j!\7280q!aD!fD36ĺ" CORRECT.":7290!p" COUNT AGAIN. THERE ARE 36."!z2:22::"RETURN";:!}7300!B$!:K1:7160L"1:10:" K3:"1:2 2:2 3:2 4:2 5:2 6:2"Y 3:K4:"1:3 2:3 3:3 4:3 5:3 6:3" *3:K5:"1:4 2:4 3:4 4:4 5:4 6:4" 43:K6:"1:5 2:5 3:5 4:5 5:5 6:5" >3:K7:"1:6 2:6 3:6 4:6 5:6 6:6" H_!R:" NOT MORE LIKELY THAN OTHERS."92:22::"RETURN";:D7150LB$f6700:K7:7160:72503:K:"R:G R:G R:G R:G R:G R:G"3:K1:"---------------------------------" 3:K2:"1:1 2:1 3:1 4:1 5:1 6:1"( 3:-------";!I212:MUS(I)0:IiK1100:6830:MUS(TROLL)MUS(TROLL)1:23TROLL:9:MUS(TROLL):K1:12:" ALMOST CERTAINLY THE SUMS OF 6,7, AND 8 ARE THE ONES WHICH OCCURRED MOST OFTENIN THE SIMULATION. NOW LET'S FIND OUT WHY SOME SUMS ARE"----------------------------------------";c1:7:"*SUMS *2 *3 *4 *5 *6 *7 *8 *9 *10*11*12*";1:8:"*-----*--*--*--*--*--*--*--*--*--*--*--*";1:9:"*TIMES* * * * * * * * * * * *"; 1:10:"---------------------------------TURN TO SEE THE DICE ROLL."&!6980.&B$806830D1:14:" THE COMPUTER WILL NOW ROLL THE PAIR OF DICE 100 TIMES AND KEEP TRACK OF ALL OF THE SUMS THAT ARE OBTAINED. TO SEE THIS HAPPEN PRESS RETURN."N7010XB$b6700,1:6:" PROBABILITY CONCERNING A PAIR OF DICE IS A LITTLE MORE DIFFICULT AND MUCH MORE INTERESTING THAN THE PROBABILITY INVOLVING ONE DIE. THIS COMPUTER CAN""SIMULATE THE ROLLING OF A PAIR OF DICE. LISTEN FOR THE SOUND OF THE DICE.""PRESS RE" # ":X:3:"# #"::6868O:X:1:"###":X:2:" ":X:3:"###"::6868u36:23:(16336):36:23:" "|IJ16:5:" "TROLLRL(1,10)RL(2,10)16:5:RL(1,10);" + ";RL(2,10);" = ";TROLL683063,6864,6865,6866F:X:1:" ":X:2:" # ":X:3:" "::6868{:X:1:"# ":X:2:" ":X:3:" #"::6868:X:1:"# ":X:2:" # ":X:3:" #"::6868:X:1:"# #":X:2:" ":X:3:"# #"::6868:X:1:"# #":X:2:YS(1,3,OR 5), THE REQUIRED PROBABIL-ITY IS 3/6 OR 1/2.":6780`r:" YOUR ANSWER IS CORRECT."z|2:22::"RETURN";:6790B$6900J110I12DICE(6(1)1)RL(I,J)DICE:X15:I2X20DICE6861,6862,68NOTHER ONE. WHAT IS THE PROBABILITY THAT AN ODD NUMBER WILL TURN UP";WE6760_JB$pOB$""ī6760TK6755:230^ANS12ī6770`6760c=h:" SINCE THE DIE CAN TURN UP IN 6 WAYS AND SINCE AN ODD NUMBER CAN TURN UP IN 3 WA:18:"6 : 4"t615:19:"5 : 1":25:19:"6 : 6":"NOW WHAT IS THE PROBABILITY THAT YOU WILL GET AN EVEN SUM";682106B$6B$""ī82106819062:22::"RETURN";:682356B$:82356K8205:2306 ANS12ī82207 821":25:11:"2 : 6":15:12:"1 : 3":25:12:"3 : 5"}515:13:"2 : 2":25:13:"4 : 4":15:14:"3 : 1":25:14:"5 : 3"515:15:"1 : 5":25:15:"6 : 2":15:16:"2 : 4":25:16:"4 : 6" 615:17:"3 : 3":25:17:"5 : 5":15:18:"4 : 2":25.":8180481604t4" YOUR ANSWER IS NOT CORRECT. PRESS RETURN TO SEE A TABLE WHICH MAY HELP YOU."42:22::"RETURN";:481644B$47500:15:9:"R : G":25:9:"R : G":15:10:"-----":25:10:"-----"5515:11:"1 : 1:22:"THE CORRECT ANSWER IS 5/36."B330:22::"RETURN";:M38110U3B$37500:1:10:" WHAT IS THE PROBABILITY THAT YOU GET AN EVEN SUM";381603B$3B$""ī81603K8155:2304ANS12ĺ:" THAT IS CORRECT. VERY GOOD7:16:"2 : 4"E2l17:17:"3 : 3":17:18:"4 : 2":17:19:"5 : 1"2r1:20:" NOW WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM OF 6";2w80902|B$2B$""ī80902K8085:2302ANS536ĺ" THAT'S CORRECT.":8100280902'3 6";1E80401JB$(1OB$""ī804081TK8035:230c1^ANS536ĺ:" THAT'S CORRECT.":8100m1`8040s1c1h1:11:" NO. HERE IS A TABLE WHICH SHOWS THE WAYS YOU CAN GET A SUM OF 6."2j17:13:"R : G":17:14:"-----":17:15:"1 : 5":17990 0B$0B$""ī7990-0"K7985:230Q0,ANS536ĺ:" CORRECT.":7995[0.7990a0106:" NO. THE CORRECT ANSWER IS 5/36."0;2:22::"RETURN";:0<80000=B$1@7500:1:9:" WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM OF17:15:"R : G":17:16:"-----":17:17:"2 : 6":17:18:"3 : 5"{/17:19:"4 : 4":17:20:"5 : 3":17:21:"6 : 2"/2:22::"RETURN";:/7950/ B$/7500:1:10:" NOW WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM OF 8";00 .B$k.7500:1:10:" LOOK CAREFULLY AT THE TABLE ABOVE. IN HOW MANY WAYS CAN YOU GET A SUM OF 8";v.7910~.B$.B$""ī7910.(B$)5ĺ:" CORRECT.":7940.1:13:" NO. YOU CAN GET AN 8 IN 5 WAYS. LOOK AT THE TABLE BELOW."D/CORRECT SO I THINK YOU UNDERSTAND DICE PROBLEMS PRETTY WELL. LET'S MOVE ON TO ANOTHER TOPIC."y-2:22::"RETURN";:-8110-B$:8110-1:11:"CORRECT SO WE NEED TO WORK ON DICE PROBLEMS SOME MORE."-2:22::"RETURN";:.788,x22:17:"1 : 3":22:18:"2 : 1":22:19:"2 : 2":22:20:"3 : 1"x,}1:21:" THUS, THE CORRECT ANSWER IS 6/36.",2:22::"RETURN";:,7830,B$,7500:1:10:" OF THE PAST 4 QUESTIONS YOU ANSWERED ";C,C3ī7860_-1:11:"7+dANS16ĺ:" YOUR ANSWER IS CORRECT.":CC1:7810A+f7790G+i+n1:11:" YOUR ANSWER IS INCORRECT. HERE IS A TABLE WHICH SHOWS HOW YOU COULD GET A SUM LESS THAN 5."+s22:13:"R : G":22:14:"-----":22:15:"1 : 1":22:16:"1 : 2"F" NO. A SUM OF 9 CAN OCCUR IN 4 WAYS. HENCE, THE CORRECT ANSWER IS 4/36."f*22:22::"RETURN";:q*77750y*<B$*F7500:1:9:" WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM LESS THAN 5";*K7790*PB$*UB$""ī7790*ZK7785:230 ANSWER IS 2/36.",)2:22::"RETURN";:7)7680?)B$)7500:1:10:" WHAT IS THE PROBABILITY THAT YOU WILL GET A SUM OF 9";)7720) B$)B$""ī7720)K7715:230)ANS19ĺ:" CORRECT.":CC1:7730) 7720)#L*(:S THE PROBABILITY THAT YOU WILL GET A SUM OF 11";<(7650D(B$U(B$""ī7650e(K7645:230(ANS118ĺ:" YES, THAT'S RIGHT.":CC1:7670(7650():" NO, YOUR ANSWER IS WRONG. AN 11 CAN TURN UP IN 2 WAYS. HENCE, THE CORRECT 6CC1:7590'7580'':"NO. SINCE THE SUM OF 7 CAN OCCUR IN 6 WAYS AND SINCE 36 DIFFERENT SUMS ARE POSSIBLE, THE CORRECT ANSWER IS 6/36.":7600':" CORRECT."'2:22::"RETURN";:'7610'B$1(7500:1:10:" WHAT I8340 : : :" NO. SINCE EACH POSSIBLE SUM WITH A PAIR OF DICE IS GREATER THAN 1, THE CORRECT ANSWER IS 36/36 OR 1.": 2:22::"RETURN";:: 470: B$:470 J HAT THE EVENT CANNOT OCCUR."79X 2:22::"RETURN";:B9] 8300J9b B$9l 7500:1:10:" WHAT IS THE PROBABILITY OF GETTING A SUM GREATER THAN 1";9q 83409v B$9{ B$""ī83409 K8335:2309 ANS1ĺ:" CORRECT. VERY GOOD.":8350: 8- 827080 B$$82 B$""ī8270G85 (B$)0ĺ:" CORRECT.":8280W8: K8265:230x8D ANS0ĺ:" CORRECT.":82808F 82708I 9N :" SINCE IT IS IMPOSSIBLE TO GET A SUM OF 13 THE CORRECT ANSWER IS 0. REMEMBER THAT A PROBABILITY OF 0 MEANS T107 d7 7500:1:10:" THERE ARE 18 WAYS YOU CAN GET AN EVEN SUM. THUS, THE ANSWER IS 18/36."n7 82307 7500:2:9:" CORRECT."7& 2:22::"RETURN";:7' 82357( B$8+ 7500:1:10:" WHAT IS THE PROBABILITY OF GETTING A SUM OF 13";:"RETURN";:!8660 !B$*!8673z!J1322:1:J:" ":40:J:" ";:J:!:14:1:"PENNY : DIME":14:2:"------------":16:3:"H : H"!16:4:"H : T":16:5:"T : H":16:6:"T : ILS."A!:" NOW WHAT IS THE PROBABILITY OF GETTINGTWO TAILS";L!8640T!B$e!B$""ī8640u!K8635:230!ANS14ĺ:" CORRECT.":8650!8640!!" SORRY, YOUR ANSWER IS NOT CORRECT. THE CORRECT ANSWER IS 1/4." !30:22:1:13:" WHAT IS THE PROBABILITY OF GETTING TWOTAILS";Ck!8590Kp!B$\u!B$""ī8590lz!K8585:230!ANS14ĺ:" CORRECT.":8650!8590!!" NOTICE THAT IN THE TABLE THERE ARE FOUR POSSIBILITIES AND ONLY ONE OF THESEHAS TWO TAENIENCE SAKE WE WILL ASSUME THAT ONE IS A PENNY AND ONE IS A DIME. THE TABLE BELOW LISTS THE POSSIBLEOUTCOMES."R!14:6:"PENNY : DIME":14:7:"------------":16:8:"H : H"\!16:9:"H : T":16:10:"T : H":16:11:"T : T"8f! !"LIKELY TO OCCUR AS THE OTHER THE PROB- ABILITY OF GETTING A HEAD IS 1/2. SIMI-"*!"LARLY, THE PROBABILITY OF GETTING A TAILIS ALSO 1/2."4!2:22::"RETURN";:6!85109!B$s>!:1:" NEXT LET'S CONSIDER FLIPPING TWO COINS. FOR CONV929:I:3:"#":I:20:"#":IB J419:9:J:"#";:29:"#":JS I17000:I !:4:" WE WILL NOW INVESTIGATE PROBLEMS IN- VOLVING COINS. IF WE FLIP ONE COIN"!"THERE ARE TWO POSSIBLE OUTCOMES, A HEAD OR A TAIL. SINCE EACH OUTCOME IS AS"T00,500,500,500,500,500,560,565,570,575,580,585A0"RUN PART.7"T5"RUN PART.8"g:"RUN PART.9"{?"RUN PART.10"D"RUN PART.11"I"RUN PART.12" *PART 6, COINS* :14:6:"PROBABILITY":17:10:"PART 6":17:15:"COINS" IUN PART.1""RUN PART.2"0"RUN PART.3"C "RUN PART.4"V"RUN PART.5"&:" PLEASE PUT DISKETTE II IN THE DISK ANDPRESS RETURN."(554)B$*:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."..N5NT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISK."N510,515,520,525,530,8400 "RNOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"p "PRESS ";::"RETURN";::".";z 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"x"YOU WA0,550,550J :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;:". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."L :" WOULD YOU LIKE TO WORK ON ALE BAG-COMPLEX"L " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N504,504,504,504,504,8400,550,550,550,55MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MARB$,LLM)) ,DEN0K% 1ANSNUMDEN+ 61 @O J *LIST OF PROGRAM PARTS* T" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT YOU MAY DO ONE OR"I h"{2 *PART.6*<N6$FB$(10).Z8400r **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**~L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((B!! ! ! ! ! !!!!!!!!!""" " " " " """""""""S AND ONE WITH THREE TAILS. THUS, THE CORRECT ANSWER IS 4/8."]&L$2:22::"RETURN";:h&M$9295p&N$B$y&O$470 B HUS, THE CORRECT ANSWER IS 4/8."&L$2:22::"RETURN";:&M$9295&N$B$&O$470 470 ITY OF GETTING AT LEAST TWO TAILS (IN THIS CASE AT LEAST 2 MEANS 2 OR 3.)";W%'$9290_%,$B$p%1$B$""ī9290%6$K9285:230%@$ANS12ĺ:" YES. WELL DONE.":9292%B$9290%E$C&J$:" THERE ARE THREE LINES IN THE TABLE WITH EXACTLY TWO TAIL HEADS";$#9230$#B$,$#B$""ī9230<$#K9225:230_$$ANS38ĺ:" CORRECT.":9240i$$9230o$ $$$:" NO. THE CORRECT ANSWER IS 3/8."$$2:22::"RETURN";:$$9245$$B$$$:I1:8920L%"$8670:1:13:" WHAT IS THE PROBABIL" CORRECT. VERY GOOD."!##9240'##k##:" NO. HERE IS WHAT THE TABLE SHOULD LOOKLIKE.":I12000:I##:I1:8920:2:13$#" NOW FIND HOW MANY WAYS YOU CAN HAVE EXACTLY TWO HEADS. AGAIN, WHAT IS THE PROBABILITY OF GETTING EXACTLY TWO WITH THREE TAILS. THUS, THE CORRECT ANSWER IS 4/8."S"#2:22::"RETURN";:^"#9110f"#B$w"#216,0:9295"#:" WHAT IS THE PROBABILITY OF GETTING EXACTLY TWO HEADS";"#9170"#B$"#B$""ī9170"#K9165:230##ANS38ĺ:EAST TWO TAILS? (IN THIS CASE AT LEAST 2 MEANS 2 OR 3.)";D!P#9080L!Z#B$]!_#B$""ī9080m!d#K9075:230!n#ANS12ĺ:" CORRECT. WELL DONE.":9100!p#9080!s#9"x#" THERE ARE THREE LINES IN THE TABLE WITH EXACTLY TWO TAILS AND ONE ENTRY HEADS"; #9020 #B$+ ##B$""ī9020; (#K9015:230\ 2#ANS38ĺ" CORRECT.":9025f 4#9020l 7# <#" THE CORRECT ANSWER IS 3/8." A#2:22::"RETURN";: C#9030 D#B$9!F#:I1:8920:1:12:" WHAT IS THE PROBABILITY OF GETTING AT L""ī8980#K8975:230F #ANS38ĺ:" CORRECT. VERY GOOD.":9025P #8980V##" YOUR ANSWER IS INCORRECT. NOTICE OUT OF THE 8 ENTRIES IN THE TABLE, 3 OF" #"THEM HAVE EXACTLY TWO HEADS. NOW WHAT ISTHE PROBABILITY OF GETTING EXACTLY TWO : T : T"3"11:I6:"T : H : H"U"11:I7:"T : H : T"w"11:I8:"T : T : H""11:I9:"T : T : T":"1:13:" WHAT IS THE PROBABILITY OF GETTING EXACTLY TWO HEADS";"8980"B$"B$HE TABLE AND THE TABLE SHOULD LOOK LIKE THIS."C"I3:8920:8940"9:I:"PENNY : DIME : QUARTER":9:I1:"----------------------""11:I2:"H : H : H""11:I3:"H : H : T""11:I4:"H : T : H""11:I5:"HYES, THERE SHOULD BE 8 LINES IN THE TABLE AND YOUR TABLE IS PROBABLY COR- RECT."n"2:22::"RETURN";:y"9130"B$:9130":" NO, YOUR ANSWER IS INCORRECT.":2:22::"RETURN";:"8910"B$/":" THERE SHOULD BE 8 LINES IN TMES. YOUR COLUMNS SHOULD BE HEADED LIKE THE TABLE BELOW."|"9:9:"PENNY : DIME : QUARTER":J1114:15:J:": :":J"9:10:"----------------------""1:16:" HOW MANY LINES ARE IN YOUR TABLE";"8900"A"A8ī8900T":" : k"8815l"B$jo":" NEXT LET'S CONSIDER FLIPPING THREE COINS. FOR CONVENIENCE SAKE WE WILL"t""ASSUME THEY ARE A PENNY, A DIME, AND A QUARTER. ON A PIECE OF PAPER COMPLETE"9~""A TABLE LISTING ";::"ALL";::" OF THE POSSIBLE":"OUTCO8800 B"B$0G"(B$)0ĺ:" CORRECT.":8810AI"B$""ī8800QL"K8995:230rV"ANS0ĺ:" CORRECT.":8810|X"8800["`":" SINCE IT IS IMPOSSIBLE TO GET THREE HEADS WITH ONE TOSS OF TWO COINS THE ANSWER IS 0."j"2:22::"RETURN";7:"PENNY : DIME":14:18:"------------":16:19:"H : T":16:20:"T : H"$"" THUS, THE REQUIRED PROBABILITY IS 2/4.";."2:22::"RETURN";:0"87603"B$8"8670:1:13:" WHAT IS THE PROBABILITY OF GETTING THREE HEADS";="T"J!1:13:" WHAT IS THE PROBABILITY OF GETTING EXACTLY ONE HEAD";U!8720]!B$n!B$""ī8720~!K8715:230"ANS12ĺ:" CORRECT.":8750"8720 """ THERE ARE TWO WAYS TO GET EXACTLY ONE HEAD AS SHOWN BELOW."S"14:1