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NOVEMBER 1979.. >LXV LAST MOD. JULY 1979^`tj ' RANDOM TEST 'z'APUTE")"AND PRINT THE RESULTS"::255_"...SHALL I START? (YES=1,NO=0) ";A1:A11ī9999h100$K10000ĺ:"WHY DON'T YOU TAKE A NAP?":"OR GET SOMETHING TO EAT?...OR BOTH?.255:88B GIVEN TO APPLE CORE OF SAN FRANCISCO TO CONTINUE...>"((16384)155890@(16384)160950R16368,0::n COMPUTE TIME REQUIRED100:"ONCE I START""IT WILL TAKE ME ABOUT "KB1;" SECONDS""WHICH IS ";(KB1)60;" MINUTES""OR ";(KB1)3600;" HOURS TO COM* *":/:CT$"* RANDOM DISTRIBUTION *":850MCT$"AUTHOR UNKNOWN":850jCT$"NOVEMBER 1979":850CT$"PROGRAM TO DETERMINE THE DISTRIBUTION":850CT$"OF RANDOM NUMBERS":85021:" PRESS THE 'ESC' TO END""< PRESS THE SPACE BAR25);U;" %"->5);"9 TO 10= ";J;25);V;" %">CI110::IHE::eF PROGRAM OF NOV.1979 BYnH950MK0:K10:K20:45R PRINT CENTER ROUTINEW20(CT$)2\CT$a""fz16368,0:16298,0:::10:10:"* * * THE END * O 2 = ";B;25);N;" %"8 5);"2 TO 3 = ";C;25);O;" %"[ 5);"3 TO 4 = ";D;25);P;" %"~ 5);"4 TO 5 = ";E;25);Q;" %" 5);"5 TO 6 = ";F;25);R;" %" 5);"6 TO 7 = ";G;25);S;" %" *5);"7 TO 8 = ";H;25);T;" %" 45);"8 TO 9 = ";I;100 Q(EK)100$ R(FK)1004 S(GK)100D T(HK)100T U(IK)100d V(JK)100j p  "TOTAL OF RANDOM NUMBERS SAMPLED ";K  "NUMBERS FROM: PERCENTAGE OF TOTAL:" 5);"0 TO 1 = ";A;25);M;" %" 5);"1 T 550 HH1 550% II1. 5508 JJ1A 550R &K1ABCDEc 0K2FGHIJt :K1K2K590 ?"COMPUTING...SAMPLES LEFT TO GO = ";K(K1K2) B936 D100 N936 XM(AK)100 bN(BK)100 lO(CK)100 vP(DK) X2280 X3310% X43402 X5370? X6400L X7430Y X8460f X9490t X10520 X10520 AA1 550 BB1 ,550 6CC1 J550 TDD1 h550 rEE1 550 FF1 550 GG1"SAMPLE SIZE ? ";K 7F <"WANT NUMBERS PRINTED? (1=YES,0=NO) ";LP B936m FL1B1.110:1000::80 KB1.097:1000:100 P"NUMBERS PRINTED IN SEQUENCE AS GENERATED" Z dX((1)10) xL1140 "RANDOM NUMBER = ";X X1250 { 16368,0:16298,0::< PROGRAM TO DETERMINE THEY DISTRIBUTION OF RANDOM NUMBERS ON A 1 TO 10 BASIS#CT$(40):900(-A0:B0:C0:D0:E0:F0:G0:H0:I0:J0:K0:L0:M0:N0:O0:P0:Q0:R0:S0:T0:U0:V0: 2      70 "ENTER THE NUMBER OF PEOPLE IN THE GROUP"7N?C0G(P1Q2A365[7B365i<P(AB)PsFCC1PCN110ZAA1d60nP1Px"THE PROBABILTY THAT NO TWO PEOPLE IN A GROUP OF "N" HAVE THE SAME BIRTHDAY IS "P" z #?Xò    !"Ǡ٠͠Ԡ ŠϠɠ ٠̠Π̠Ӡ Ӡ ŠϠР ؠڠ̾٠Šm :936+"AMS GRADES 4-12 "= D$(13)(4)D5d"PROBABILITY & STATISTICS":"EDUCATIONAL PROGRAMS FOR THE APPLE"15"COLLECTED AND DISTRIBUTED BY": :"APPLE FOR THE TEACHER & ABC SOFTWARE " !"2331 RAINBOW  gW'  `^ :F Y %^LǏLZ^[_\Z][`1''I8Mt_=gH?J QVQT_ɕ%[^ZZ\[]^Z_[ 0W Г J1  @)ȹ@)ȹ@) q P^ɠ 0   qL MW'WП < XX QLiLLs4         Y11:X1,Y2:XX1:YY2% < ****************M FINAL DROPU 15^ X,Yl A12:1w X,YA~ A ****************** NEW BALL1:19,415:19,4:1:19,5X19:Y5 :50'::(13)(4)"CATALOG"-E******************U LEFT MOVE]15fX,Yv1:X1,Y115:X1,Y11:X1,Y2:XX1:YY2$***************** RIGHT MOVE15X,Y1:X1,Y115:X1,";\X039fSX,Y)&pB$(S);8zX:"!";::Ys"-----------------------------------------": 41-'S4:L6581:" ";(L);:L:0:34,22:936:23:"DO YOU WANT TO MAKE ANOTHER RUN(Y/N)?";A$A$"Y"960A$"N"970920S DRAW GRAPH"1:X1CS117:Q(C(S)F):Q0790V (40Q),39X2oXX2:S:R$"N"920{ B$(15)*B$(0)" ":B$(1)"X":I215:B$(I)" ":I41::>"-----------------------------------------": 41-'SHY039R"!TURN FOR THE GRAPH";:A$4 ROUTINE TO DRAW GRAPHX DRAW BACKGROUND AND LABELd::15pA0390,38A:A3:21:L6581:" ";(L);:L CHECK TO SEE IF DATA WILL FIT GRAPHS117C(S)C(S1)HC(S):F(H40)1NTER. THEN PRESS RETURN."$ &A$:1, 0:Q :10)"RESULTS OF ";BA;" BALLS":v D3:S117:(64S);". ";:C(S), NS::0:R$"Y"640 X: b10)"RESULTS OF ";BA;" BALLS": l3:S117:15:(64S);". ";:C(S) vS:24:"PRESS RE TA 936:23:"FINISHED. PRESS RETURN FOR RESULTS.";:A$\  PRINTING OF RESULTSd : 5:5:"DO YOU WANT TO MAKE A COPY OF THE" :8:"RESULTS ON A PRINTER (Y/N) ?";R$ R$"Y"540 R$"N"600 480 :"TURN ON THE PRIP$(P) J(P$)3P$P$" "6 T(P$)2P$P$" "O ^(P$)1P$P$" " h23:"BALLS TO DROP= ";P$;:21:"BALLS DROPPED= ";T rS9:4000 |W116 M(2(1)1) M1SS.5:2000 M2SS.5:1000 W C(S)C(S)1 3000A0382 A,38:A,39:A/ MAIN PROGRAM: C(17)\ 3:21:L6581:" ";(L);:Lg 34,22 "1:23:"HOW MANY BALLS DO YOU WANT TO DROP?";BA$:BA(BA$) ,BA1BA10000Ė36:" ":290 6936:R((78)256(79)) @T1BA:PBAT:"TO DROP 55 BALLS."8 Z15:"PRESS RETURN WHEN READY.";@ nA$V x DRAW BACKGROUND` :15l A039{ 0,38A:A 12 0,390:0,391:0,3937:0,3938 B6344:A3352 A,B:A:B B8364 A2362 A,B:A:B  ** ICTM 1981 **1 *** BALLDROP ***7O BY MARLYS NEWCOMEUk HARRISON SCHOOL# WONDER LAKE, IL60097( SEPT 1981-2:<5:7:"THIS IS A BALL DROP PROGRAM."F:8:"IT TAKES ABOUT ONE MINUTE" P:12:     00 N0 (X((1)61)' 2V(X)11 <NN1< FK16K PV(K)040R ZKY _Nc dTTNn nK16y xV(K)0 K I "AVERAGE = ";T100 COMPUTER WILL SHOW HOW MANY"S "TOSSES IT TOOK FOR EACH ":"OF 100 REPETITIONS"~ "OF THIS EXPERIMENT"::T115000:T1 "AT THE END, IT WILL PRINT OUT THE" "AVERAGE NUMBER OF TOSSES PER" "TRIAL. ":::T615000:T6 T0 I111"DO YOU WANT INSTRUCTIONS(Y/N)?":A$@A$"N"28OA$"Y"10r:"TYPE Y FOR YES, N FOR NO."y2  "THIS PROGRAM SIMULATES REPEATED" "TOSSES OF A DIE UNTIL ALL SIX" "NUMBERS APPEAR."::T1110000:T1: "THE  A$A$(13)640 &DKED." &T511500:T5 0@ :"EACH TIME, THE FINAL TOTAL"X D"WILL BE PRINTED."k NT511500:T5q X b"AT THE END, A TABULATION OF HOW OFTEN" l"EACH FINAL TOTAL OCCURRED " q"WILL BE PRINTED." v "HIT TO CONTINUE."RST EXCEEDS 20." ) T513000:T52 125X "WHAT IS THE MOST LIKELY FINAL "| "TOTAL THAT WILL BE OBTAINED?"  255 T512000:T5 "THIS PROGRAM WILL PERFORM THIS" "EXPERIMENT AS MANY TIMES AS YOU" "CHOOSE WHEN ASX; 9X(X)ĺ".0"; :" %"' @I1O J:"DO YOU WANT TO TRY AGAIN(Y/N)?"W TA$g ^A$"N"390v hA$"Y"72 r:"TYPE Y FOR YES, N FOR NO.": |330 :"BYE"   "A DIE IS ROLLED REPEATEDLY UNTIL" "THE RUNNING TOTAL FI:' "FINAL NUMBER OF PER-"L "TOTAL OCCURRENCES CENT"X I116i " ";I120;~ V(I1)100ĺ" "; V(I1)10ĺ" "; " "; "V(I1); ," "; 1X(V(I1)N8)100 2X10ĺ" "; 7X((X10))10 8 MN8( NN8100N8(N8)N8100075N O:100:"O.K. HERE WE GO."::255Z PA1N8b ZS0t dX((1)52) nI1X xY(1) Y.5150 Y(1) I R((1)61) SSR S20160 S, V(S20)V(S20)1 A ( V(6) 7 "DO YOU WANT INSTRUCTIONS(Y/N)?"?A$NA$"Y"70](A$"N"72c23"TYPE Y FOR YES, N FOR NO."4510F410HI116IV(I1)0JI1K"HOW MANY REPETITIONS DO YOU"L"WANT DONE(FROM 100-1000)?"     A! "NUMBER OF MATCHES IS ";M> "OUT OF";MN;" TRIALS"D (THAT A MATCH OCCURRED.":0 ::T115000:T1; V(25)G M0:N0S A1Q1_ (K125s 2X((1)3651)~ <V(K)X FK PI124 ZJI125 dV(I)V(J)145 nJ xI }"NO MATCH" NN1 160 "MATCH" MM1 0:T4:b "HOW MANY TRIALS WOULD YOU":"LIKE TO HAVE DONE(PICK A":"NUMBER FROM 1 TO 100)?":Q1 Q11Q1100Q1(Q1)4 :"THE PROGRAM WILL INDICATE IF THERE WAS":"A MATCH OR NOT FOR EACH OF":"THE"Q1;"TRIALS AND TOTAL THE NUMBER":"OF TIMES FO:"THIS PROGRAM SIMULATES REPEATED":"TRIALS OF THE BIRTHDAY PROBLEM.":"ASSUME THAT THERE ARE 25 PEOPLE":"IN A ROOM WITH RANDOM BIRTHDAYS." "IF TWO HAVE THE SAME BIRTHDAY,":"THERE IS A MATCH; OTHERWISE, THERE":"IS NO MATCH.":T41800   TIMES":"THAT THE FIRST ONE WAS RED.":F "PROBABILITY = ";S(SF)L R160& x"YOU GOT GREEN FIRST, SO WE "G y"IGNORE IT AND START AGAIN"[ z:T11400:T1d 160 "YOU GOT RED THEN RED" :T11400:T1 SS1 A "GIVEN RED THE FIRST TIME," "YOU GOT A SECOND RED ";S( "TIMES OUT OF ";SF;"ILL BE LISTED":"AT THE END."::T117000:T1X 25:"THE PROGRAM BEGINS NOW.":255:` S0h F0u A1100 (X((1)3) 2X0120 <X1140 FY((1)23) PY3120 Z"YOU GOT RED THEN GREEN" [:T11400:T1 dFF1 n ALSO RED?"::T117000:T1 "THIS PROGRAM WILL SIMULATE 100":"TRIALS OF THIS EXPERIMENT; IT WILL":"PRINT OUT THE RESULTS OF EACH TRIAL,":"TABULATE HOW OFTEN THE SECOND":"MARBLE WAS RED IF THE FIRST ONE":"WAS ALSO RED.". :"THE FINAL TOTALS WONE BOX IS PICKED AT RANDOM AND":"ONE OF THE TWO MARBLES IN IT IS":"CHOSEN. IF THIS MARBLE IS GREEN,":"WE START OVER."::"THE PROBLEM IS: IF THE FIRST MARBLE":"CHOSEN IS RED, WHAT IS THE" "PROBABILITY THAT THE OTHER MARBLE":"IN THAT SAME BOX ISN8:"DO YOU WANT INSTRUCTIONS(Y/N)?":A$:A$"N"10"THERE ARE THREE BOXES."::"ONE BOX CONTAINS TWO RED MARBLES.":"ONE BOX CONTAINS ONE RED":"AND ONE GREEN MARBLE.":"THE THIRD BOX CONTAINS":"TWO GREEN MARBLES.":T116000:T1: "     "TYPE Y FOR YES, N FOR NO."$ ,250* @: J"SO LONG."@ TF : A, "YOU WON A TOTAL OF ";TL "DOLLARS IN ";Q;" TRIALS."R s "AVERAGE WINNINGS ARE ";TQ " DOLLARS." :T512000:T5 "DO YOU WANT TO TRY AGAIN(Y/N)?" A$ A$"Y"ė A$"Y"41 A$"N"320  "0 iZ nZN170 x180* TT250Q "YOU WIN $250":S1110:(7):S1b Z11000:Zk 180w TT100 " YOU WIN $100":S1110:(7):S1 Z11000:Z 180 TT50 " YOU WIN $50":S1110:(7):S1 Z11000:ZER OF TRIALS?";Q: *"PICK YOUR NUMBER FROM 1 TO 500? ";NH +N50042T ,N142d -(N)N42o /A1Q 0X((1)5001) 1X;" ";:XN130 2Y((1)5001) <YX50 AY;" "; FYN150 PZ((1)5001) ZZX80 dZY8;:T513000:T5_ :"FIRST PRIZE IS $250, SECOND PRIZE":"IS $100, AND THIRD PRIZE IS $50."r $T513000:T5 &:"THIS PROGRAM SIMULATES REPEATED":"TRIALS OF THE LOTTERY TO SEE":"HOW MUCH YOU WIN AND SHOWS THE":"WINNING NUMBERS.": )"NUMBB-"DO YOU WANT INSTRUCTIONS(Y/N)?"5A$;JA$"Y"26Y A$"N"41z "TYPE Y FOR YES, N FOR NO."5"THERE IS A LOTTERY WITH 500 TICKETS":"NUMBERED 1-500.":"YOU HAVE ONE TICKET WITH ANY NUMBER" "YOU CHOOSE."     ";T6500 "S CENT" : " 21 ";T1;" ";T1500d " 22 ";T2;" ";T2500 " 23 ";T3;" ";T3500 " 24 ";T4;" "T4500 " 25 ";T5;" ";T5500 " 26 ";T6;" R((1)61) SSR( (S20200 -S,T 2(S20)110,120,130,140,150,100e dT6T61:160v nT1T11:160 xT2T21:160 T3T31:160 T4T41:160 T5T51 A : "FINAL NUMBER OF PER-" "TOTAL OCCURRENCE"OF THIS EXPERIMENT AND PRINT THE":"FINAL TOTAL EACH TIME.": "AT THE END, A TABULATION OF THE":"NUMBER OF TIMES EACH FINAL TOTAL":"OCCURS WILL BE SHOWN.":: Z110000:Z 25 "THE PROGRAM BEGINS NOW." 255 A1500 S08:"DO YOU WANT INSTRUCTIONS(Y/N)?":A$:A$"N"10GA$"Y"1"A DIE IS ROLLED REPEATEDLY UNTIL":"THE RUNNING TOTAL FIRST EXCEEDS 20."::"WHAT IS THE MOST LIKELY FINAL TOTAL?":::T112000:T1? "THIS PROGRAM WILL DO 500 REPETITIONS":    R1 S T(S)T(S)1 ,P< 6"SUM # OF TIMES":H @K111Y JK;15);T(K)` TKf ^"D." T215000:T2# P11009 Z114:V(Z)0:ZI S0:R0:G0T A15g X((1)141)v (V(X)130 2V(X)1 <A FT16 PV(T)0100 ZRR1 dT nT714 xV(T)0140 GG1 T R16R G18G SGȺ"BOX AND THE NUMBER OF REDS IN THE"p "GREEN BOX."::"THIS PROGRAM WILL DO THIS 100 TIMES.":T1110000:T1 :"THE PROGRAM WILL PRINT OUT THIS" "TOTAL FOR EACH TRIAL AND WILL":"SHOW A TABULATION OF HOW MANY TIMES":"EACH FINAL TOTAL OCCURREhV(14):T(12)d"THERE ARE 6 RED AND 8 GREEN":"MARBLES IN A BAG.":T113000:T1::"PICK 5 AT RANDOM AND PUT""THEM IN A RED BOX. THE OTHER 9 GO""IN A GREEN BOX. FIND THE TOTAL OF"$ "THE NUMBER OF GREENS IN THE RED ":   CH FEWER THAN":" 5 WERE CHOSEN IS ";L:. ,@ T11100:T1F L  "THIS TIME IT TOOK ";N;" CHOICES":"UNTIL AN 8 OR ABOVE WAS CHOSEN." N51030 T1N:(7):T T111000:T1  T11500:T1  $ OCHOSEN THIS TIME ARE":2 X((1)151):X;",";< NN1I X8205R 170\ 1000i N5240s MM1| 250 LL1 A  "IN 100 TRIALS,": "THE NUMBER IN WHICH 5 OR MORE":"WERE CHOSEN IS ";M:( ""THE NUMBER IN WHI COMPUTER WILL DO 100 TRIALS":"OF THIS EXPERIMENT. AT THE END,":"YOU WILL SEE THE TOTAL NUMBER OF":"TIMES THAT 5 OR MORE WERE TAKEN.":T115000:T1: n20: x"THE PROGRAM BEGINS NOW." 255 L0:M0 A1100 N0 "THE NUMBERS TOTAL OF 5 ":"OR MORE BALLS?":T115000:T1:6 Fn P"THIS PROGRAM WILL SIMULATE THIS":"EXPERIMENT.": Z"IT WILL SHOW WHAT NUMBERS WERE":"SELECTED AND THE NUMBER OF DRAWINGS":"DONE BEFORE AN 8 OR ABOVE IS SELECTED.":T117000:T1: d"THE"A MAN DRAWS A BALL.":T114000:T1} (:"IF ITS NUMBER IS LESS THAN 8, HE":"REPLACES IT AND DRAWS AGAIN.":T114000:T1 2:"IF THE NUMBER IS 8 OR GREATER, HE":"STOPS.":T114000:T1:0 <"THE QUESTION IS: WHAT IS THE":"PROBABILITY HE DRAWS A9:"DO YOU WANT INSTRUCTIONS(Y/N)?":A$:A$"N"140HA$"Y"10k"TYPE Y FOR YES OR N FOR NO."~W111000:W12 :"A SET OF 15 POOL BALLS BEARING":"THE NUMBERS 1 TO 15 INCLUSIVE":"IS PLACED IN A BAG."T113000:T1:$      ((1)201)8E(X)01070)BE(X)50LC;VC15N`X((1)201)`jE(X)01120ktE(X)1r~CxW218W219230+" ";W2;15);W(W21)3W2I:T1110000:T1r"TOTAL WON = ";T0;" IN 100 TRIALS.""AVERAGE WON = ";T0100N120:E(N)0:NC12X((1)201)E(X)01020E(X)10C$C13 .X170 W1E(EN)E(EM)1? :"AMOUNT WON THIS TRIAL= ";W11N T0T0W11` W(W1)W(W1)1g Am "AMOUNT WON ";10);"# OF TIMES" W2020 W23W24230 W27W28W29230 W212W213230 W214W216W217230Z"TOTAL IS ";E(EN)E(EM);" DOLLARS."G d"DO YOU WANT TO TRY AGAIN?"O nA$U sd xA$"Y"10j } "NOW THE COMPUTER WILL DO 100":"TRIALS OF THIS EXPERIMENT." T00 A1100 1000 EN((1)201) EM((1)201) ENEM' ("THAT CONTAINS ";E(EN);" DOLLARS."- -B 2"PICK ANOTHER."J <EMW >EM166e ?EM2066w @EM(EM)66 A70 B:"NO GOOD. YOU HAVE TO PICK AN":"INTEGER FROM 1 TO 20." C60 FENEM50 P"THAT HAS ";E(EM);" DOLLARS." U& EXPERIMENT.":# T115000:T1:6 :E(20),W(21)@ 1000x "PICK AN ENVELOPE(I.E. A NUMBER":"FROM 1 TO 20.)"~  EN EN136 !EN2036 "EN(EN)36 #40 $:"NO GOOD. YOU MUST PICK AN INTEGER":"FROM 1 TO 20." %30H. THE OTHER TEN HAVE":"BLANK PAPER IN THEM.":T115000:T1 :"YOU CHOOSE TWO ENVELOPES AND":" WIN WHATEVER IS IN THEM."::T114000:T1 "YOU MAY DO THIS AS MANY TIMES AS YOU":"LIKE. THEN THE COMPUTER WILL":"SIMULATE 100 TRIALS OF THIS":"z7:"DO YOU WANT INSTRUCTIONS(Y/N)?":A$:A$"N"9EA$"Y"5{"PRINT Y FOR YES OR N FOR NO.":W111000:W1:1= :"THERE ARE 20 ENVELOPES ON A TABLE.":"TWO CONTAIN $10 BILLS. THREE":"CONTAIN $5 BILLS. FIVE OF THEM":"CONTAIN $1 EAC     ^"THIS TIME, X= ";B1D_"THE NUMBER OF GOOD ONES CHOSEN= ";G1W`:W1125:W1ohB2(B11)B2(B11)1vrA|" X # OF TIMES"N0M" ";N;11);B2(N1)NT1(D1)1160 T1(D1)1# N. N1P@ X((1)T1)M N1260[ Q11N1m XP1(Q1)210u Q1 P1(N)X N N1P V1P1(N) "T1(V1)1330 ,G1G11 @340 JB1B11 TN UI91350 V"X= ";B1W360P"AT THE END, YOU WILL GET A TABULATION":"OF HOW OFTEN EACH VALUE OF X":"OCCURRED.":W117000:W1l Ry ZPD120 dMD n130 xMP T1(T),P1(P),B2(M1) A1100 N51T:T1(N5)0:N5 G10:B10 N1D D1((1)T1) MANY WILL BE SELECTED EACH TIME?":P:W113000:W1:B =I9190 F"THE COMPUTER WILL DO THE EXPERIMENT":"100 TIMES."::"LET X= THE NUMBER OF DEFECTIVE":"CHOSEN IN A GIVEN TRIAL. THE VALUE OF":"X WILL BE PRINTED EACH TIME.": HW114000:W1f E":"BOX EACH TIME.":W116000:W16 W113000:W1h (:"HOW MANY TRANSISTORS ARE IN THE BOX":T: 2"HOW MANY ARE DEFECTIVE?":D: 7DT58 860 :"NO. THE NUMBER DEFECTIVE HAS TO BE":"LESS THAN THE NUMBER IN THE BOX."::505 <"HOW NSISTORS":"WILL BE RANDOMLY SELECTED FROM THE":"BOX AND WE WILL SEE HOW MANY OF THOSE" "SELECTED ARE DEFECTIVE.":W115000:W1# :"YOU PICK (1)THE NUMBER IN THE BOX,":"(2)THE NUMBER WHICH ARE DEFECTIVE,":"AND(3)HOW MANY WILL BE PICKED FROM TH7:"DO YOU WANT INSTRUCTIONS(Y/N)?":A$:A$"N"4FA$"Y"10z"TYPE Y FOR YES OR N FOR NO.":W41800:W4:1I9140X :"THERE IS A BOX WITH SOME TRANSISTORS":"IN IT. A FEW OF THESE TRANSISTORS ARE":