' +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$3>L[dmx- ( { Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(` d ֠z# u`z!#??     ϠԮԮ ԮԮԮԮ8! HELLO PROGRAM DISKETTE IID TOM HAMEL AND ERNIE WOODWARDY COPYRIGHT 1982r( APPLE II PLUS, 48K2:14:4:"PROBABILITY"<19:6:"BY"F5:9:"T. R. HAMEL AND E. L. WOODWARD"P6:12:"AUSTIN PEAY STATE UNIVERSITY"% Z4:1!.%95500%B$"5%B$""ī95502:%K9545:230RD%ANS12ĺ:" GOOD.":9560\F%9550bI%N%:" NO. SINCE THERE 26 CARDS THAT ARE CLUBS OR DIAMONDS THE CORRECT ANSWER IS 26/52 OR 1/2."X%2:22::"RETURN";:]%9570_%B$@b%9500HE DECK THE CORRECT ANSWER IS 4/52 OR 1/13.":9510%I1122:1:I:" ":40:I:" ";:I:&%2:22::"RETURN";:(%9515)%B$+%9500:1:12:" WHAT IS THE PROBABILITY THAT IT IS A CLUB OR A DIAMOND"; 40 $B$$9500M$1:12:" WHAT IS THE PROBABILITY THAT IT IS A 5";X$9490`$B$q$B$""ī9490$K9485:230%ANS113ĺ:" YES, YOU ARE CORRECT.":9510 %9490 %2%:" SORRY, YOU ARE WRONG. SINCE THERE ARE FOUR 5'S IN TTHE PROBABILITY THAT IT IS A SPADE";0$94208$B$I$B$""ī9420Y$K9415:230|$ANS14ĺ:" CORRECT.":9430$9420$$:" NO. THERE ARE 13 SPADES AND THUS THE CORRECT ANSWER IS 13/52 OR 1/4."$2:22::"RETURN";:$94"THAT AN ORDINARY DECK OF 52 PLAYING CARDS HAS FOUR SUITS(CLUBS,DIAMONDS, HEARTS,AND SPADES). EACH SUIT HAS THE"$"FOLLOWING CARDS: 2,3,4,5,6,7,8,9,10, JACK,QUEEN,KING,AND ACE. SUPPOSE ONE CARD IS DRAWN AT RANDOM."%$1:12:" WHAT IS :13:"PLAYING":17:16:"CARDS"Fr$I929:I:3:"#":I:20:"#":Ijw$J419:9:J:"#";:29:"#":J{y$I17000:I|$:" IN ORDER TO SATISFACTORILY COMPLETE THIS SECTION YOU MUST KNOW SOMETHING ABOUT ORDINARY PLAYING CARDS. REMEMBER"x$K.";.N500,500,500,500,500,500,9300,565,570,575,580,585N5"RUN PART.8"a:"RUN PART.9"u?"RUN PART.10"D"RUN PART.11"I"RUN PART.12"T$ ** PART 7 **^$ ** PLAYING CARDS **h$:14:6:"PROBABILITY":17:10:"PART 7" m$16";N:"TO BE LOADED FROM THE DISK."AN510,515,520,525,530,535T"RUN PART.1"g"RUN PART.2"z"RUN PART.3" "RUN PART.4""RUN PART.5""RUN PART.6"*:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DISNT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484:" PLEASE PUT DISKETTE I IN THE DISK AND PRESS RETURN."504B$":" PLEASE WAIT A FEW SECONDS FOR PART NOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"p "PRESS ";::"RETURN";::".";z 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"x"YOU WA4,554,554J :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;:". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."L :" WOULD YOU LIKE TO WORK ON ALE BAG-COMPLEX"L " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N500,500,500,500,500,500,9300,554,554,55MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MARB$,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.7*<N7$FB$(10).Z9300r **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**~L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((B       ::"RETURN";:%9690"%B$+%470 :9680%9670%%:" NO. THERE IS ONLY ONE CARD WHICH IS BOTH A CLUB AND A 10 SO THE CORRECT ANSWER IS 1/52."%2:22::"RETURN";:%9690%B$%470 B%B$%470 A 10 SO THE CORRECT ANSWER IS 1/52."%2:22 10OF CLUBS. THUS, THE CORRECT ANSWER IS 16/52 OR 4/13."T%2:22::"RETURN";:_%9630g%B$%9500:1:12:" WHAT IS THE PROBABILITY THAT IT IS A CLUB AND A 10";%9670%B$%B$""ī9670%K9665:230%ANS152ĺ:" YES.":1:12:" WHAT IS THE PROBABILITY THAT IT IS A CLUB OR A 10";Kg%9610Sl%B$dq%B$""ī9610tv%K9605:230%ANS413ĺ:" VERY GOOD.":9620%9610%:%:" THERE ARE 13 CLUBS AND 4 10'S IN THE DECK. HOWEVER, ONE OF THE 10'S IS THE+11300,B$# ,B$""ī113004,K11295:230X,ANS49ĺ:" CORRECT.":11310c,11300i,$," THE POSSIBLE PRIME NUMBERS ARE 2,3,5, AND 7. THE CORRECT ANSWER IS 4/9.".,2:22::"RETURN";:0,113203,B$<8,11190:1:8:" WHCORRECT.":11310+11240!++" YOUR ANSWER IS NOT CORRECT. IT MAY BE THAT YOUR DEFINITION OF PRIME IS NOT CORRECT. A PRIME NUMBER IS A NUMBER"+"WITH EXACTLY TWO DIVISORS. TRY AGAIN. WHAT IS THE PROBABILITY THAT THE NUMBER IS PRIME"; +11180+B$)+11190:1:8:11200x+J822:1:J:" ":40:J:" ";:J:+" WHAT IS THE PROBABILITY THAT THE NUM- BER IS PRIME";+11240+B$+B$""ī11240+K11235:230+ANS49ĺ:" AT THE COR- RESPONDING NUMBER IS ODD";2u+11160:z+B$L+B$""ī11160]+K11155:230+ANS59ĺ:" CORRECT.":11170+11160++:" NO. SINCE 1,3,5,7, AND 9 ARE ODD NUM- BERS THE CORRECT ANSWER IS 5/9."+2:22::"RETURN";: 9 *"H+32:7:"*******"dR+1:1:" SUPPOSE WE HAVE A CONTAIN-":"ER THAT HAS 9 SLIPS OF PAPER"\+"IN IT NUMBERED 1,2,3,4,5,6,7,":"8, AND 9. SUPPOSE THAT ONE"f+"PIECE OF PAPER IS SELECTED":"AT RANDOM.":1:8&p+" WHAT IS THE PROBABILITY TH17:13:"NUMBER":17:16:"CARDS"G+I929:I:3:"#":I:20:"#":Ik+J419:9:J:"#";:29:"#":J|+I17000:I +4+30:1:"* *":31:2:"* 1 2 3 *":31:3:"* *">+31:4:"* 4 5 6 *":31:5:"* *":31:6:"* 7 8 ISK.">.N500,500,500,500,500,500,560,11000,570,575,580,585Q0"RUN PART.7"d:"RUN PART.9"x?"RUN PART.10"D"RUN PART.11"I"RUN PART.12"* ** PART 8 **+ ** NUMBER CARDS ** +:14:6:"PROBABILITY":17:10:"PART 8"!+T ";N:"TO BE LOADED FROM THE DISK."CN510,515,520,525,530,535V"RUN PART.1"i"RUN PART.2"|"RUN PART.3" "RUN PART.4""RUN PART.5""RUN PART.6"*:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DWANT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484:" PLEASE PUT DISKETTE I IN THE DISK AND PRESS RETURN."504B$$:" PLEASE WAIT A FEW SECONDS FOR PAR ANOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"r "PRESS ";::"RETURN";::".";| 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"z"YOU 554,554,554L :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;:". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."N :" WOULD YOU LIKE TO WORK ONBLE BAG-COMPLEX"M " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N500,500,500,500,500,500,554,11000,554,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MARB$,LLM)) ,DEN0K& 1ANSNUMDEN, 62 @P J *LIST OF PROGRAM PARTS* T" FOLLOWING IS A LIST OF PROGRAM PARTS. IT IS RECOMMENDED THAT YOU GO THROUGH" ^"THESE PARTS IN ORDER. THE PARTS ARE LISTED HERE SO THAT YOU MAY DO ONE OR"J h2 *PART.8*<N8$FB$(10)/Z11000s **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((          22::"RETURN";:&~.11910&&.B$/&.470 IORRECT.":11900 %^.K11885:230B%h.ANS1ĺ:" CORRECT.":11900M%j.11890S%m.%r.:" NO. SINCE ALL 16 OF THESE NUMBERS ARE LESS THAN 50 THE CORRECT ANSWER IS 16/16OR 1."%|.2:22::"RETURN";:%~.11910%.B$%.470 B6/16OR 1."&|.2:8.11840$;.B$_$@.J1122:1:J:" ":40:J:" ";:J$J.1:11:" WHAT IS THE PROBABILITY THAT THE NUM- BER FORMED IS LESS THAN 50";$O.11890$T.B$$V.B$""ī11890$X.(B$)1ī11870%Y.(B$)1ĺ:" C""ī11820#.K11815:230I#".ANS14ĺ:" CORRECT. VERY GOOD.":11830T#$.11820Z#'.#,.:" NO. THE NUMBERS FROM THE LIST WHICH ARE DIVISIBLE BY 11 ARE 11,22,33, AND 44. THUS, THE CORRECT ANSWER IS 4/16 OR 1/4."#6.2:22::"RETURN";: $SOMETHING LIKE THIS:"R"-10:6:"11 21 31 41":10:7:"12 22 32 42""-10:8:"13 23 33 43":10:9:"14 24 34 44"".1:11:" WHAT IS THE PROBABILITY THAT THE NUM- BER FORMED IS DIVISIBLE BY 11";" .11820".B$ #.B$IS MEANS THAT NUMBERS LIKE 22 AND 33 ARE POSSIBLE. ON SCRATCH PAPER LIST ALL POSSIBLE NUMBERS."z!-2:22::"RETURN";:!-11740!-B$!-J222:1:J:" ":40:J:" ";:J"-1:3:" YOUR LIST SHOULD LOOK -11690 -B$Q -:10:1::"1";:15:1:"2";:20:1:"3";:25:1:"4": -:" NEXT LET'S CONSIDER THE CASE WHERE THESLIPS ARE NUMBERED 1,2,3, AND 4 AS BE- FORE BUT THIS TIME THE FIRST SLIP IS"`!-"RETURNED BEFORE THE SECOND IS SELECTED. THz-B$""ī11670:}-(B$)0ĺ:" THAT'S RIGHT.":11680K-K11665:230r-ANS0ĺ:" THAT'S RIGHT.":11680}-11670--:" NO. SINCE THERE ARE 0 NUMBERS WHICH ARE BETWEEN 25 AND 30 THE CORRECT ANS- WER IS 0." -2:22::"RETURN";: 43 ARE THE ONLY NUMBERS IN THE LIST WHICH ARE GREATER THAN 35, THE CORRECT ANSWER IS 3/12 OR 1/4."d-2:22::"RETURN";:i-11630k-B$n-11190:1:8:" WHAT IS THE PROBABILITY THAT THE NUM- BER IS BETWEEN 25 AND 30";s-11670x-B$1:5:"14 24 34 43"u2-1:8:" WHAT IS THE PROBABILITY THAT THE NUM- BER THAT IS FORMED IS GREATER THAN 35?"<-11610A-B$F-B$""ī11610K-K11605:230P-ANS14ĺ:" CORRECT.":11620R-11610U-gZ-:" NO. SINCE 41,42, AND A PIECE OF"c,"SCRATCH PAPER LIST ALL OF THE POSSIBLE TWO DIGIT NUMBERS THAT COULD BE FORMED."},2:22::"RETURN";:,11540-B$-:" YOUR LIST SHOULD LOOK LIKE THIS:"-11:3:"12 21 31 41":11:4:"13 23 32 42"(-1T NUMBER IS FORMED BY USING THE FIRST DIGIT SELECTED AS THE TEN'S DIGIT AND THE SECOND DIGIT SE- LECTED AS THE UNIT'S DIGIT. FOR EXAMPLE,"; ,"IF THE FIRST DIGIT SELECTED IS 2 AND THE SECOND DIGIT SELECTED IS 4, THE NUMBER WOULD BE 24. ON THE SITUATION WHERE THERE AREFOUR SLIPS OF PAPER NUMBERED 1,2,3, AND 4. SUPPOSE NOW THAT TWO SLIPS OF PAPER","ARE SELECTED WITHOUT REPLACEMENT. THIS MEANS THE SECOND SLIP IS SELECTED WITH- OUT REPLACING THE FIRST SLIP. SUPPOSE","THAT A TWO DIGINS1ĺ:" YES.":11430",11420(,,:" NO. SINCE EACH POSSIBLE NUMBER IS LESSTHAN 10, THE CORRECT ANSWER IS 9/9 OR 1.",2:22::"RETURN";:,11440,B$,:10:1::"1";:15:1:"2";:20:1:"3";:25:1:"4":m,:" CONSIDERANSWER IS 0."'j,2:22::"RETURN";:3l,11380;o,B$t,11190:1:8::" WHAT IS THE PROBABILITY THAT THE NUM- BER IS LESS THAN 10";y,11420~,B$,B$""ī11420,(B$)1ī11400,(B$)1ĺ:" YES.":11430,K11415:230,AAT IS THE PROBABILITY THAT THE NUM- BER IS GREATER THAN 10";H=,11360PB,B$bD,B$""ī11360G,(B$)0ĺ:" CORRECT.":11370L,K11355:230V,ANS0ĺ:" CORRECT.":11370X,11360[, `,:" NO. SINCE THIS CANNOT HAPPEN, THE COR-RECT 3K13235:23033ANS110ĺ:" CORRECT.":13250>313240D33" NOTICE THAT THERE ARE 20 ENTRIES IN THE TABLE AND EXACTLY TWO ENTRIES IN- VOLVE TWO BLUE MARBLES. THUS, THE PROB- ABILITY IS 2/20 OR 1/10."32:22::"RETURN";:31323195:23003ANS110ĺ:" WELL DONE.":13250;313200A33" NO. TRY AGAIN. LOOK FOR THOSE OCCUR- RENCES IN THE TABLE WHEN BOTH MARBLES ARE BLUE. WHAT IS THE PROBABILITY THAT BOTH MARBLES ARE BLUE";3132403B$3B$""ī132402B1 R3B1 B1R3 B2R3"KJ34:A3:"R1B2 R2B2 R3B2 B1B2 B2B1":eT32:22::"RETURN";:qY313150y[3B$^3A1::13100:1:6h3" WHAT IS THE PROBABILITY THAT TWO BLUE MARBLES ARE DRAWN";m313200r3B$w3B$""ī13200 |3K1 R1,R2,R3 AND THE BLUE MARBLES BE REPRE- SENTED BY B1 AND B2. FOLLOWING IS A LISTOF ALL OF THE POSSIBLE OUTCOMES."3A15:13100:13140,34:A:"R1R2 R2R1 R3R1 B1R1 B2R1"634:A1:"R1R3 R2R3 R3R2 B1R2 B2R2"@34:A2:"R1B1 R~2"ALSO, THE MARBLES ARE DRAWN WITHOUT RE- PLACEMENT, THAT IS, THE SECOND MARBLE ISDRAWN WITHOUT PUTTING THE FIRST MARBLE"3"BACK IN THE BAG. WE WANT TO LIST ALL OF THE POSSIBLE OUTCOMES. FOR CONVENIENCE"t3"LET THE RED MARBLES BE REPRESENTED BY:13:"MARBLE BAG":16:16:"COMPLEX"K2I929:I:3:"#":I:20:"#":Io2J419:9:J:"#";:29:"#":J2I17000:I2:" SUPPOSE THAT A MARBLE BAG CONTAINS 3 RED MARBLES AND 2 BLUE MARBLES. TWO MAR-BLES ARE DRAWN AT RANDOM FROM THE BAG."ISK.">.N500,500,500,500,500,500,560,565,13000,575,580,585Q0"RUN PART.7"d5"RUN PART.8"x?"RUN PART.10"D"RUN PART.11"I"RUN PART.12"2 *PART 9*2 *MARBLE BAG-COMPLEX*2:14:6:"PROBABILITY":17:10:"PART 9"%214T ";N:"TO BE LOADED FROM THE DISK."CN510,515,520,525,530,535V"RUN PART.1"i"RUN PART.2"|"RUN PART.3" "RUN PART.4""RUN PART.5""RUN PART.6"*:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THE DWANT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484:" PLEASE PUT DISKETTE I IN THE DISK AND PRESS RETURN."504B$$:" PLEASE WAIT A FEW SECONDS FOR PAR ANOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"r "PRESS ";::"RETURN";::".";| 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"z"YOU 554,554,554L :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;:". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."N :" WOULD YOU LIKE TO WORK ONBLE BAG-COMPLEX"M " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N500,500,500,500,500,500,554,554,13000,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. MARB$,LLM)) ,DEN0K& 1ANSNUMDEN, 62 @P 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"J hy2 *PART.9*<N9$FB$(10)/Z13000s **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN((          2 R2B1 R2B2 R3B1 R3B2"@ &5" B1R1 B1R2 B1R3 B2R1 B2R2 B2R3"Z *52:22::"RETURN";:f -513620n 05B$w 45470 B05B$ 45470 5" B1R1 B1R2 B1R3 B2R1 B2R2 B2R3" *52:22::"RETURN";: -513620 05B$ 45470 IR";4136005B$)5B$""ī13600: 5K13595:230`5ANS1225ĺ:" CORRECT.":13610k513600q5 5:" SORRY, YOUR ANSWER IS WRONG. NOTE THATA RED MARBLE AND A BLUE MARBLE (EITHER ORDER) CAN BE DRAWN IN 12 WAYS." #5:" R1B1 R1B THE CORRECT ANSWER IS 6/25."742:22::"RETURN";:C413550K4B$4J722:1:J:" ":40:J:" ";:J41:7:" WHAT IS THE PROBABILITY THAT ONE RED MARBLE AND ONE BLUE MARBLE ARE DRAWN IN EITHER ORDE30 4B$4B$""ī13530-4K13525:230O4ANS625ĺ:" GOOD.":13540Z413530`44:" NO. NOTE THAT THERE ARE 6 WAYS THAT A RED MARBLE COULD BE DRAWN FIRST AND THENA BLUE MARBLE."::" R1B1 R1B2 R2B1 R2B2 R3B1 R3B2"4:" THUS,HE TABLE AND 4 IN WHICH BOTH MARBLESDRAWN ARE BLUE, THE CORRECT ANSWER IS 4/25."l42:22::"RETURN";:x4134804B$4:A1:1337041:7:" WHAT IS THE PROBABILITY THAT A RED MARBLE IS DRAWN FIRST AND THEN A BLUE MARBLE";41352 B2B2":^l41:15:" IN THIS CASE WHAT IS THE PROBABILITY OF DRAWING TWO BLUE MARBLES";jq413460rv4B${4B$""ī134604K13455:2304ANS425ĺ:" CORRECT.":134704134604R4:" NO. SINCE THERE ARE 25 TOTAL ENTRIES IN TOWS:"04A9:13370:13420I:44:A:"R1R1 R2R1 R3R1 B1R1 B2R1"yD44:A1:"R1R2 R2R2 R3R2 B1R2 B2R2"N44:A2:"R1R3 R2R3 R3R3 B1R3 B2R3"X44:A3:"R1B1 R2B1 R3B1 B1B1 B2B1" b44:A4:"R1B2 R2B2 R3B2 B1B" AGAIN LET'S ASSUME WE HAVE A BAG WITH 3 RED AND 2 BLUE MARBLES. LET'S ALSO AS-SUME THAT TWO MARBLES ARE DRAWN FROM THEBAG BUT THIS TIME SUPPOSE THE FIRST"4"MARBLE IS REPLACED BEFORE THE SECOND ONE IS DRAWN. NOW THE POSSIBLE OUTCOMES ARE AS FOLLT. VERY GOOD.":13320 313310&33:" SORRY, YOUR ANSWER IS NOT CORRECT. IN THE TABLE YOU WILL FIND 6 ENTRIES WHICH REPRESENT DRAWING 2 RED MARBLES. HENCE, THE CORRECT ANSWER IS 6/20 OR 3/10."42:22::"RETURN";: 413330 4B$4:60 3B$W3J622:1:J:" ":40:J:" ";:J31:6:" WHAT IS THE PROBABILITY THAT TWO RED MARBLES ARE DRAWN";3133103B$3B$""ī133103K13305:2303ANS310ĺ:" YOUR ANSWER IS CORREC"THE SCORE 8-8 OR":"7-9. SINCE THESE TWO":"OUTCOMES ARE EQUALLY":"LIKELY THE REGION";"FOR THE 7-9 OUTCOME":"IS THE SAME SIZE AS":"THE REGION FOR THE":"8-8 OUTCOME.";" PRESS ";::"RETURN";::" TO SEE THESE REGIONS.";;15130;B$9:J11716:I:J:"-":J:IF[;I233916:J216:I:J:":":J:I|`;23:1:"*":39:1:"*":23:17:"*":39:17:"*"j;1:7:" WE CAN ANSWER THIS":"QUESTION BY DRAWING":"PICTURES. WITH THE"t;"SCORE AT 7-8, ONE":"MORE FLIP WILL MAKE"X~;I*.;I233916:J216:I:J:":":J:IO8;29:5:"8 - 8":29:13:"7 - 9"B;J1178:23:J:"*":39:J:"*":J:15250L;:" IF THE SCORE IS 7":"TO 8 IN FAVOR OF B,":"WHAT IS THE PROBA-"Q;"BILITY THAT A WILL":"WIN THE GAME?"V;I233FICULT QUESTION AND WE DO NOT EXPECT YOU TO BE ABLE TO ANS- WER IT WITHOUT SOME HELP. TO GET SOME HELP WITH THIS QUESTION PRESS ";::"RETURN";::".":2:22::"RETURN";::15180;B$;15180;I2339:J1178$;I:J:"-":J:PED AND WHEN A HEAD COMES UP PLAYER A GETS A POINT. LIKEWISE, PLAYER B GETS A POINT WHEN":"A TAIL COMES UP. NOW HERE IS THE QUES- TION. IF THE SCORE IS 7 TO 8 IN FAVOR OFB, WHAT IS THE PROBABILITY THAT A WILL WIN?"::" THIS IS A VERY DIF"A GAME".:I929:I:3:"#":I:20:"#":IR:J419:9:J:"#";:29:"#":Jc:I17000:I::" WE WILL NEXT CONSIDER A GAME IN WHICH TWO PEOPLE (LET'S CALL THEM A AND B) AREFLIPPING A COIN. THE GAME GOES AS FOL-"_:"LOWS. THE COIN IS FLIP DISK."@.N500,500,500,500,500,500,560,565,570,15000,580,585S0"RUN PART.7"f5"RUN PART.8"y:"RUN PART.9"D"RUN PART.11"I"RUN PART.12": *PART 10*: *CSMP GAME*::14:6:"PROBABILITY":16:10:"PART 10":16:15:ART ";N:"TO BE LOADED FROM THE DISK."EN510,515,520,525,530,535X"RUN PART.1"k"RUN PART.2"~"RUN PART.3" "RUN PART.4""RUN PART.5""RUN PART.6"*:" PLEASE WAIT A FEW SECONDS FOR PART ";N:"TO BE LOADED FROM THEU WANT TO RETURN AT A LATER TIME RE- MEMBER WHICH PARTS YOU HAVE COMPLETED. PLEASE TURN OFF THE MACHINE AT THIS TIME."484:" PLEASE PUT DISKETTE I IN THE DISK AND PRESS RETURN."504B$&:" PLEASE WAIT A FEW SECONDS FOR PON ANOTHER PARTOF THE PROGRAM? ANSWER ";::"YES";::" OR ";::"NO";::" AND"t "PRESS ";::"RETURN";::".";~ 480 B$ (B$,1)"Y"ė:400 :" REMEMBER THAT YOU JUST COMPLETED PART":N;" OF THE PROGRAM. IN THE EVENT THAT"|"YO15000,554,554N :"YOU MADE AN ERROR INPUTTING A NUMBER. TRY AGAIN.":400 :" YOU HAVE JUST COMPLETED PART ";N;:". IF":"YOU HAVE AT LEAST 10 MORE MINUTES YOU MAY WISH TO WORK ON ANOTHER PART OF THE PROGRAM."P :" WOULD YOU LIKE TO WORK ARBLE BAG-COMPLEX"O " 10. A GAME":" 11. LOOKING BACK":" 12. SELF TEST" :" ENTER THE NUMBER OF THE PART YOU WANT TO INVESTIGATE AND THEN PRESS THE ";::"RETURN";::" KEY."; 460 N:N500,500,500,500,500,500,554,554,554,"MORE OF THESE PARTS NOW AND THEN FIN- ISH THE PROGRAM AT A LATER TIME." :" 1. INTRODUCTION":" 2. MARBLES IN A BAG":" 3. SPINNER":" 4. PARACHUTIST":" 5. DICE" " 6. COINS":" 7. PLAYING CARDS":" 8. NUMBER CARDS":" 9. M(B$,LLM)) ,DEN0K( 1ANSNUMDEN. 64 @R 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"L h2 *PART.10*<N10&FB$(10)1Z15000u **ROUTINE FOR CONVERTING FRACTIONS FROM STRINGS TO DECIMALS**L(B$)KI1L(B$,I,1)"/"ī270ILMIL0īKNUM((B$,LM1))LML1DEN1:300 "DEN(           =:" NO. THE CORRECT ANSWER IS 5/16."D"=2:22::"RETURN";:P"=15780X"=B$a"=470 4BILITY THAT A WILL WIN";&!m=15760.!r=B$@!w=B$""ī15760Q!|=K15755:230x!=ANS516ĺ:" VERY GOOD.":15770!=15760!=!=:" NO. THE CORRECT ANSWER IS 5/16."!=2:22::"RETURN";:!=15780!=B$!=470 N=B$!=4705695:2300 J=ANS516ĺ:" VERY GOOD.":15770; L=15700A O= T=1:11:" WE CAN BREAK THE":"BIG RECTANGLE UP INTO":"16 SMALL RECTANGLES." ^="OF THOSE 16 RECTANGLES":"5 REPRESENT A WIN FOR":"A. NOW TRY AGAIN.":1:18!h=" WHAT IS THE PROBA:I;=37:11:"W":37:15:"L":35:13:"*":39:13:"*"U"=2:22::"RETURN";:a$=15660i'=B$,=15270:1:7:" NOW WHAT IS THE":"PROBABILITY THAT A":"WILL WIN";1=157006=B$7=23:9:"*-------*---*---*";=B$""ī15700 @=K1S"b<"LIKELY TO WIN AS THE":"OTHER SO THE REGION":"IS SEPARATED INTO":"EQUALLY SIZED PARTS."<1:21:" PRESS ";::"RETURN";::" TO SEE THESE REGIONS.";<15620M" (D) 5/8"!?M" (E) 7/8"!CM19800"DM2:22:B HEAD AND ONE TAIL?". M" (A) 1/3"@ M" (B) 1/4"R M" (C) 1/2"d M" (D) 3/4"t M" (E) 1" M19750 M2:22:B$ M(B$)65ī19750 !M(B$)70ī19760 &M1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":19730!0MSL19700L2:22:B$.L(B$)65ī19700CL(B$)70ī19710L1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":19680LSTUD$(STUD$,6)B$(STUD$,8): M1:4:"8. IF TWO COINS ARE FLIPPED WHAT IS THE PROBABILILTY OF GETTING ONE22:" ":196309LSTUD$(STUD$,5)B$(STUD$,7):L1:4:"7. IF YOU TOSS A PAIR OF DICE WHAT IS THE PROBABILITY YOU WILL GET A SUM OF 8?"L" (A) 1/36"L" (B) 2/36"L" (C) 3/36"L" (D) 4/36"L" (E) 5/36" IS THE PROBABILITY THAT YOU WILL GET A 3?"HL" (A) 1/12"ZL" (B) 1/6"lL" (C) 3/6"~L" (D) 5/6"L" (E) 1"L19650L2:22:B$L(B$)65ī19650L(B$)70ī19660L1:21:"INVALID ANSWER. TRY AGAIN.":2: (D) 11/16"!wL" (E) 14/16"-{L19600<|L2:22:B$QL(B$)65ī19600fL(B$)70ī19610L9:22:"INVALID ANSWER. TRY AGAIN.":2:22:" ":19580LSTUD$(STUD$,4)B$(STUD$,6):5L1:4:"6. IF YOU TOSS ONE STANDARD DIE WHAT AGAIN.":2:22:" ":19530OhLSTUD$(STUD$,3)B$(STUD$,5):TP14:19180rL1:14:"5. WHAT IS THE PROBABILITY THAT THE PARACHUTIST FALLS IN REGION 'A' AND REGION 'B'?"sL" (A) 3/16"tL" (B) 5/16"uL" (C) 6/16" vL"ARACHUTIST FALLS IN REGION 'A' OR REGION 'B'?"IAL" (A) 3/16"]BL" (B) 10/16"qCL" (C) 11/16"DL" (D) 14/16"EL" (E) 15/16"IL19550JL2:22:B$TL(B$)65ī19550YL(B$)70ī19560^L9:22:"INVALID ANSWER. TRY L" (E) 14/16"L19500+L2:22:B$@"L(B$)65ī19500U'L(B$)70ī19510,L1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":194806LSTUD$(STUD$,2)B$(STUD$,4):TP14:191806@L1:14:"4. WHAT IS THE PROBABILITY THAT THE P:J:"!":J5KI15273:J1133:I:J:"*":J:IUL16:5::"A":26:5:"B":L1:14:"3. WHAT IS THE PROBABILITY THAT THE PARACHUTIST FALLS IN REGION 'A'?"L" (A) 3/16"L" (B) 7/16"L" (C) 9/16"L" (D) 10/16"I1518:I:13:"-":I2KJ113:15:J:":":JNKJ1013:18:J:":":JiKJ110:24:J:":":JKI1827:I:4:"+":IKI1821:I:7:"+":IKI2127:I:13:"+":IKJ47:18:J:"!":JKJ713:21:J:"!":J KJ413:27D$,20):6`O1:4:"20. SUPPOSE THAT EACH TIME YOU ATTEMPT A PARTICULAR TASK THE PROBABILITY THAT YOU WILL BE SUCCESSFUL IS 0." 7aO" IF YOU WERE TO ATTEMPT THIS TASK 100 TIMES, ABOUT HOW MANY TIMES WOULD YOU EXPECT TO BE SUC?"50O" (A) 0"$51O" (B) 5"652O" (C) 20"H53O" (D) 50"[54O" (E) 100"g57O20300v58O2:22:B$5BO(B$)65ī203005GO(B$)70ī203105LO1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":202806VOSTUD$(STUD$,18)B$(STU4.O1:4:"19. SUPPOSE THAT EACH TIME YOU ATTEMPT A PARTICULAR TASK THE PROBABILITY THAT YOU WILL BE SUCCESSFUL IS 1."5/O" IF YOU WERE TO ATTEMPT THIS TASK 100 TIMES, ABOUT HOW MANY TIMES WOULD YOU EXPECT TO BE SUCCESSFUL (A) 0"3N" (B) 1/2"/3O" (C) 20"A3O" (D) 50"T3O" (E) 100"`3O20250o3O2:22:B$3O(B$)65ī202503O(B$)70ī202603O1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":202304$OSTUD$(STUD$,17)B$(STUD$,19)::"18. SUPPOSE THAT EACH TIME YOU ATTEMPT A PARTICULAR TASK THE PROBABILITY THAT YOU WILL BE SUCCESSFUL IS 1/2."2N" IF YOU WERE TO ATTEMPT THIS TASK 100 TIMES, ABOUT HOW MANY TIMES WOULD YOU EXPECT TO BE SUCCESSFUL?" 3N"1N" (B) 1/4"%1N" (C) 1/2"81N" (D) 3/4"I1N" (E) 1"U1N20200d1N2:22:B$y1N(B$)65ī202001N(B$)70ī202101N1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":201801NSTUD$(STUD$,16)B$(STUD$,18):{2N1:4NG A GAME IN WHICH A COIN IS FLIPPED. WHEN A HEAD COMES UP A GETS ONE POINT AND"0N" WHEN A TAIL COMES UP B GETS ONE POINT. IF THE SCORE IS 8 TO 9 IN FAVOR OF B, WHAT IS THE PROBABILITY THAT A WILL WIN?"0N" (A) 0"36"/N" (D) 2/6")/N" (E) 4/6"5/N20150D/N2:22:B$Y/N(B$)65ī20150n/N(B$)70ī20160/N1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":20130/NSTUD$(STUD$,15)B$(STUD$,17):Z0N1:4:"17. SUPPOSE A AND B ARE PLAYIND 2 WHITE MARBLES. IF THE FIRST MARBLE IS DRAWN AND THEN REPLACED IN THE BAG AND A SECOND MARBLE IS DRAWN, WHAT IS".N" THE PROBABILITY THAT BOTH MARBLES ARE WHITE?".N" (A) 2/36".N" (B) 2/30"/N" (C) 4/ (E) 8/9"-oN20100&-pN2:22:B$;-zN(B$)65ī20100P-N(B$)70ī20110-N1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":20080-NSTUD$(STUD$,14)B$(STUD$,16):.N1:4:"16. SUPPOSE THAT A MARBLE BAG CONTAINS 4 RED MARBLES A"15. SUPPOSE A MARBLE BAG CONTAINS 4 RED, 3 BLUE, AND 2 WHITE MARBLES. IF ONE MARBLE IS DRAWN AT RANDOM WHAT IS THE PROBABILITY THAT IT IS BLUE OR WHITE?",gN" (A) 3/9",hN" (B) 5/9",iN" (C) 6/9",jN" (D) 5/6" -kN" " (B) 1/6"!+7N" (C) 1/3"4+8N" (D) 2/4"G+9N" (E) 4/6"S+=N20050b+>N2:22:B$w+HN(B$)65ī20050+MN(B$)70ī20060+RN1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":20030+\NSTUD$(STUD$,13)B$(STUD$,15):,fN1:4:STUD$(STUD$,12)B$(STUD$,14):*4N1:4:"14. SUPPOSE A MARBLE BAG CONTAINS 4 RED MARBLES AND 2 WHITE MARBLES. IF ONE MARBLE IS DRAWN AT RANDOM FROM THE BAG, WHAT IS THE PROBA- BILITY THAT IT IS RED?"*5N" (A) 2"+6NBER IS AN ODD NUMBER?"))N" (A) 1/6"<)N" (B) 2/6"O)N" (C) 3/6"b)N" (D) 4/6"u) N" (E) 5/6") N20000) N2:22:B$)N(B$)65ī20000)N(B$)70ī20010) N1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":19980"**N(N" AT RANDOM BUT WITHOUT REPLACEMENT FROM THE CONTAINER. IF THE FIRST DIGIT SELECTED FORMS THE TEN'S DIGIT AND THE SECOND FORMS THE")N" UNIT'S DIGIT, WHAT IS THE PROBA- BILITY THAT THE RESULTING TWO DIGIT NUM'M(B$)70ī19960V'M1:21:"INVALID ANSWER. TRY AGAIN.":2:22:" ":19930}'MSTUD$(STUD$,11)B$(STUD$,13):(N1:4:"13. THREE SLIPS OF PAPER NUMBERED 1,2, AND 3 ARE IN A CONTAINER. SUPPOSE THAT TWO SLIPS OF PAPER ARE DRAWN"RN OFF THE MA- CHINE."#>P20640 NTHE MA- CHINE."D>P20640 0E THERE ANY SECTIONS YOU WOULD LIKE TO REDO AT THIS TIME? ANSWER ";::"YES";::" OR ";::"NO":=xP"AND PRESS ";::"RETURN";::".";=}P20620=PB$=P(B$,1)"Y"ī470>P::" THIS COMPLETES THE PROBABILITY LESSON.WE HOPE YOU HAD FUN. TU9,20"7<2P:" YOU MISSED THE FOLLOWING QUESTIONS:":;C<