10  COM Z1
20  DIM C[10,20]
30  DIM D$[10],A$[5],F$[70],C$[30],G$[10]
40  D$="OUTCOMES"
50  F$="P(A)+P(B)-P(A&B)+P(A)+P(B)+P(A)-P(A&B)+P(B)+P(A)*P(B)*P(A)"
60  V1=W5=V9=U5=K6=K7=K8=U7=Z2=R9=C4=0
70  IF Z1=4 THEN 5560
80  N9=-10
90  PRINT "DO YOU WANT INSTRUCTIONS FOR RUNNING PROBAB";
100  INPUT A$
110  PRINT 
120  IF A$="YES" THEN 160
130  IF A$="NO" THEN 730
140  GOSUB 5420
150  GOTO 90
160  PRINT "----- DEFINITIONS:"
170  PRINT 
180  PRINT "AN EXPERIMENT IS REPEATED 'Q' TIMES (Q IS LARGE)."
190  PRINT "THE NUMBER OF TIMES EVENT 'A' OCCURS IS 'R'."
200  PRINT "'R' IS CALLED AN OUTCOME OF EVENT 'A'."
210  PRINT "IF THE EXPERIMENT IS REPEATED AGAIN, AND AGAIN, MANY TIMES,"
220  PRINT "THERE IS A NUMBER, 'T', AROUND WHICH THE OUTCOMES, 'R', CLUSTER."
230  PRINT 
240  PRINT "-- EXPERIMENTAL PROBABILITY:"
250  PRINT "     THE EXPERIMENTAL PROBABILITY THAT AN EVENT 'A' OCCURS IS"
260  PRINT "     P(A) = T/Q  [P(A) = THE PROBABILITY OF 'A']."
270  PRINT 
280  PRINT "     EXAMPLE: THREE COINS ARE TOSSED 500 TIMES.  THE NUMBER"
290  PRINT "     OF TIMES THAT (2 HEADS AND 1 TAIL) OCCUR IS RECORDED."
300  PRINT "     THE EXPERIMENT IS REPEATED 5 TIMES."
310  PRINT "     THE EXPERIMENTAL PROBABILITY IS CALCULATED:"
320  PRINT "        Q = 500,  EVENT 'A' = (2 HEADS AND 1 TAIL)"
330  PRINT "        R(1)=190, R(2)=203, R(3)=172, R(4)=182, R(5)=158"
340  PRINT "        THE AVERAGE 'R' = 181;  SO T = 181."
350  PRINT "        EXPERIMENTAL PROBABILITY = P(A) = 181/500 = .362."
360  PRINT 
370  PRINT "-- THEORETICAL PROBABILITY:"
380  PRINT "     IF AN EXPERIMENT CAN RESULT IN ANY ONE OF 'N' DIFFERENT,"
390  PRINT "     AND EQUALLY LIKELY OUTCOMES, AND IF EXACTLY 'M' OF THESE"
400  PRINT "     OUTCOMES CORRESPOND TO EVENT 'A', THEN THE"
410  PRINT "     THEORETICAL PROBABILITY OF EVENT 'A' OCCURRING IS"
420  PRINT "     P(A) = M/N."
430  PRINT 
440  PRINT "     EXAMPLE: USING THE SAME EXPERIMENT, THE"
450  PRINT "     THEORETICAL PROBABILITY IS CALCULATED:"
460  PRINT "        A CORRECT SAMPLE SPACE (1=HEAD, 2=TAIL) IS:"
470  PRINT "        111, 112, 121, 122, 211, 221, 212, 222"
480  PRINT "        EVENT 'A', (2 HEADS AND 1 TAIL), OCCURS 3 TIMES; M = 3"
490  PRINT "        THE TOTAL NUMBER OF SAMPLE POINTS = 8; N = 8"
500  PRINT "        THEORETICAL PROBABILITY = P(A) = 3/8 = .375."
510  PRINT 
520  PRINT "THESE DEFINITIONS ARE USED IN THE ANALYSIS OF THE FOLLOWING"
530  PRINT "THREE TYPES OF EXPERIMENTS:"
540  PRINT 
550  PRINT "     1. TOSSING ONE COIN (MAXIMUM OF 5 TIMES)."
560  PRINT 
570  PRINT "     2. TOSSING ONE DIE (MAXIMUM OF 5 TIMES)."
580  PRINT 
590  PRINT "     3. MORE COMPLEX EXPERIMENTS, TOSSING UP TO 5 POLYHEDRA"
600  PRINT "        ANY NUMBER OF TIMES."
610  PRINT 
620  PRINT "YOU WILL DESIGN THE EXPERIMENT: THE NUMBER OF POLYHEDRA,"
630  PRINT "THE NUMBER OF SIDES ON EACH POLYHEDRON, THE NUMBER OF TOSSES"
640  PRINT "FOR EACH TRIAL, THE NUMBER OF TRIALS IN ONE EXPERIMENT, AND"
650  PRINT "THE NUMBER OF TIMES THE EXPERIMENT IS REPEATED (MAXIMUM OF 20)."
660  PRINT 
670  PRINT "KEEP THE ABOVE EXPLANATIONS FOR LATER REFERENCE."
680  PRINT 
690  PRINT 
700  T8=5
710  ENTER T8,T7,T9
720  N9=-10
730  PRINT "WHICH EXPERIMENT DO YOU WANT TO DO (1,2,OR 3)";
740  INPUT Z3
750  M5=N5=0
760  PRINT 
770  X5=0
780  GOTO Z3 OF 1280,790,950
790  IF K7=1 THEN 840
800  PRINT '10"----- TOSSING A DIE:"
810  PRINT "DESIGN THE EXPERIMENT: THE NUMBER OF TOSSES IN EACH EXPERIMENT,"
820  PRINT "THE SIDE WHICH YOU WANT FACING DOWN - EVENT 'A'."
830  K7=1
840  C2=S5=6
850  PRINT "FOR ONE TRIAL, HOW MANY TOSSES DO YOU WANT (MAXIMUM OF 5)";
860  INPUT N1
870  G9=0
880  GOSUB 5520
890  IF G9#0 THEN 850
900  PRINT 
910  PRINT "WHAT SUM DO YOU WANT ON THE DOWN SIDES";
920  INPUT N3
930  PRINT 
940  GOTO 1490
950  IF K8=1 THEN 1020
960  PRINT '10"----- TOSSING POLYHEDRA:"
970  PRINT "DESIGN THE EXPERIMENT: THE NUMBER OF POLYHEDRA, THE NUMBER OF"
980  PRINT "SIDES ON EACH ONE, THE SUM OF THE NUMBERS ON THE DOWN SIDES."
990  PRINT "THIS SUM IS EVENT 'A'.  THE DOWN SIDES ARE USED SINCE THERE"
1000  PRINT "IS NO ONE SIDE FACING UP FOR SOME POLYHEDRA."
1010  K8=1
1020  PRINT "HOW MANY POLYHEDRA DO YOU WANT TO USE (MAXIMUM OF 5)";
1030  INPUT N1
1040  G9=0
1050  GOSUB 5520
1060  IF G9#0 THEN 1020
1070  PRINT 
1080  C2=S5=100
1090  E1=1
1100  FOR I=1 TO 5
1110  S[I]=1
1120  NEXT I
1130  PRINT "HOW MANY SIDES FOR EACH POLYHEDRON?"
1140  PRINT "TYPE A NUMBER AND THE RETURN KEY FOR EACH QUESTION MARK."
1150  PRINT 
1160  FOR I=1 TO N1
1170  INPUT S[I]
1180  IF S[I]=INT(S[I]) AND S[I] >= 1 THEN 1220
1190  PRINT 
1200  PRINT "YOU HAVE INPUT AN INCORRECT NUMBER OF SIDES FOR YOUR POLYHEDRON."'10
1210  GOTO 1100
1220  E1=E1*S[I]
1230  NEXT I
1240  PRINT 
1250  IF Z2=1 THEN 4350
1260  IF Z2=2 OR Z2=3 THEN 4850
1270  GOTO 910
1280  IF K6=1 THEN 1340
1290  PRINT '10"----- TOSSING A COIN:"
1300  PRINT "DESIGN THE EXPERIMENT: THE NUMBER OF TOSSES IN ONE TRIAL,"
1310  PRINT "THE NUMBER OF HEADS YOU WANT IN EACH TRIAL - EVENT 'A', AND"
1315  PRINT "THE NUMBER OF TRIALS IN ONE EXPERIMENT."
1320  PRINT 
1330  K6=1
1340  C2=S5=2
1350  PRINT "FOR ONE TRIAL, HOW MANY TOSSES DO YOU WANT (MAXIMUM OF 5)";
1360  INPUT N1
1370  G9=0
1380  GOSUB 5520
1390  IF G9#0 THEN 1350
1400  PRINT 
1410  S=2
1420  PRINT "HOW MANY HEADS DO YOU WANT";
1430  INPUT H
1440  PRINT 
1450  N3=H+2*(N1-H)
1460  IF H <= N1 AND H >= 0 AND INT(H)=H THEN 1490
1470  PRINT "YOU HAVE INPUT AN INCORRECT NUMBER."
1480  GOTO 1420
1490  PRINT "HOW MANY SAMPLE POINTS DO YOU THINK ARE IN THE SAMPLE SPACE";
1500  INPUT E
1510  PRINT 
1520  IF S5=100 THEN 1540
1530  E1=C2^N1
1540  IF E=E1 THEN 1590
1550  IF C4=10 THEN 1770
1560  PRINT "BE SURE TO APPLY THE MULTIPLICATION PRINCIPLE.  TRY AGAIN!"'10
1570  C4=10
1580  GOTO 1490
1590  PRINT "RIGHT ON!"'10
1600  PRINT "HOW MANY TRIALS DO YOU WANT FOR ONE EXPERIMENT";
1610  INPUT N
1620  PRINT 
1630  IF N <= 1000 THEN 1740
1640  PRINT "IT WILL TAKE ABOUT"N/1000"MINUTES OF COMPUTER TIME"
1650  PRINT "IN ORDER TO PERFORM THIS EXPERIMENT."'10
1660  PRINT "WOULD YOU LIKE TO INPUT A DIFFERENT NUMBER FOR THE "
1670  PRINT "NUMBER OF TIMES THE EXPERIMENT IS TO BE PERFORMED";
1680  INPUT A$
1690  PRINT 
1700  IF A$="YES" THEN 1600
1710  IF A$="NO" THEN 1740
1720  GOSUB 5420
1730  GOTO 1650
1740  PRINT 
1750  IF N >= 1 AND N=INT(N) THEN 2000
1760  GOTO 2040
1770  PRINT "YOU GOOFED--DO YOU WANT THE SAMPLE SPACE PRINTED";
1780  INPUT A$
1790  PRINT 
1800  A5=2
1810  IF A$="NO" THEN 1850
1820  IF A$="YES" THEN 1950
1830  GOSUB 5420
1840  GOTO 1770
1850  PRINT "WOULD YOU LIKE TO TRY AGAIN";
1860  INPUT A$
1870  PRINT 
1880  IF A$="YES" THEN 1490
1890  IF A$="NO" THEN 1920
1900  GOSUB 5420
1910  GOTO 1770
1920  PRINT "THE CORRECT NUMBER OF SAMPLE POINTS IN THE SAMPLE SPACE"
1930  PRINT "IS"E1"."'10
1940  GOTO 1600
1950  IF S5#100 THEN 1980
1960  GOSUB 3780
1970  GOTO 1490
1980  GOSUB 3750
1990  GOTO 1490
2000  PRINT "HOW MANY TIMES DO YOU WANT THE EXPERIMENT REPEATED";
2010  INPUT N2
2020  PRINT 
2030  IF N2 >= 1 AND N2=INT(N2) THEN 2070
2040  PRINT "YOU HAVE INPUT AN INCORRECT NUMBER.  THE NUMBER MUST BE"
2050  PRINT "AN INTEGER >0.  NOW LET'S START OVER."'10
2060  GOTO 1600
2070  IF S5=100 THEN 2110
2080  FOR I=1 TO N1
2090  S[I]=S5
2100  NEXT I
2110  PRINT TAB(3);"NUMBER OF";TAB(14);"NUMBER OF";TAB(25);"EXPERIMENTAL";
2120  IF Z1=4 THEN 2150
2130  PRINT 
2140  GOTO 2160
2150  PRINT TAB(39);D$;TAB(50);D$;TAB(60);D$
2160  PRINT TAB(4);"OBJECTS";TAB(15);"TRIALS";TAB(26);D$;
2170  IF Z1=4 THEN 2200
2180  PRINT 
2190  GOTO 2220
2200  PRINT TAB(35);"A";TAB(40);"FOR B";TAB(49);"A UNION B";
2210  PRINT TAB(61);"(A&B)"
2220  FOR K=1 TO N2
2230  C[1,K]=C[2,K]=C[3,K]=C[4,K]=0
2240  FOR L=1 TO N
2250  S=0
2260  FOR J=1 TO N1
2270  Q[J]=INT(RND(1)*S[J])+1
2280  IF Z1=20 THEN 2300
2290  S=S+Q[J]
2300  NEXT J
2310  IF Z2=2 OR Z2=3 THEN 2390
2320  IF S=N3 THEN 2350
2330  IF S=N9 THEN 2370
2340  GOTO 2480
2350  C[1,K]=C[1,K]+1
2360  GOTO 2330
2370  C[2,K]=C[2,K]+1
2380  GOTO 2480
2390  IF Q[1]=N3 THEN 2430
2400  IF Q[2]=N9 THEN 2450
2410  IF Q[1]=N3 AND Q[2]=N9 THEN 2470
2420  GOTO 2480
2430  C[1,K]=C[1,K]+1
2440  GOTO 2400
2450  C[2,K]=C[2,K]+1
2460  GOTO 2410
2470  C[4,K]=C[4,K]+1
2480  C[3,K]=C[1,K]+C[2,K]-C[4,K]
2490  NEXT L
2500  PRINT TAB(6);N1;TAB(16);N;TAB(29);C[1,K];
2510  IF Z1=4 THEN 2540
2520  PRINT 
2530  GOTO 2550
2540  PRINT TAB(41);C[2,K];TAB(53);C[3,K];TAB(62);C[4,K]
2550  NEXT K
2560  PRINT 
2570  IF Z1=4 THEN 2600
2580  Z9=1
2590  GOTO 2610
2600  Z9=4
2610  C9=0
2620  FOR A=1 TO Z9
2630  S1=0
2640  FOR B=1 TO N2
2650  S1=S1+C[A,B]
2660  NEXT B
2670  C9=C9+1
2680  PRINT "THE EXPERIMENTAL OUTCOMES SEEM"
2690  PRINT "TO CLUSTER AROUND WHAT NUMBER ";
2700  IF Z1=4 THEN 2720
2710  GOTO 2810
2720  GOTO C9 OF 2740,2760,2780,2800
2730  GOTO 3110
2740  PRINT "FOR EVENT A";
2750  GOTO 2810
2760  PRINT "FOR EVENT B";
2770  GOTO 2810
2780  PRINT "FOR (A UNION B)";
2790  GOTO 2810
2800  PRINT "FOR (A & B)";
2810  INPUT F1
2820  PRINT 
2830  IF S1/N2=0 AND F1#0 THEN 2880
2840  IF F1>10 THEN 2870
2850  IF ABS(F1-S1/N2) <= .2 THEN 2910
2860  GOTO 2880
2870  IF ABS(F1-S1/N2) <= .75 THEN 2910
2880  PRINT "FIND THE AVERAGE OF THE EXPERIMENTAL OUTCOMES AND TRY AGAIN!"
2890  PRINT 
2900  GOTO 2680
2910  IF Z1=4 THEN 2930
2920  PRINT "CONGRATULATIONS!  NOW,"
2930  PRINT "** WHAT IS THE EXPERIMENTAL PROBABILITY";
2940  INPUT P1
2950  PRINT 
2960  IF ABS(F1/N-P1)<.01 THEN 3050
2970  IF U5>1 THEN 3020
2980  PRINT "GO OVER YOUR CALCULATIONS AND REFER BACK TO THE DEFINITION OF""EXPERIMENTAL PROBABILITY.  TRY AGAIN!"'10
2990  PRINT 
3000  U5=U5+1
3010  GOTO 2930
3020  PRINT "THE CORRECT EXPERIMENTAL PROBABILITY IS"F1"/"N"OR"F1/N
3030  PRINT "TRY TO DO A BETTER JOB NEXT TIME."'10
3040  GOTO 3070
3050  IF Z1=4 THEN 3070
3060  PRINT "CORRECT."
3070  A5=1
3080  PRINT 
3090  U5=0
3100  P[A]=P1
3110  NEXT A
3120  IF Z1=4 THEN 3260
3130  IF E1 <= 5000 THEN 3260
3140  IF E1>5000 AND E1 <= 10000 THEN 3250
3150  PRINT '10"THIS EXPERIMENT WILL TAKE ABOUT"E1/5000"MINUTES OF"
3160  PRINT "COMPUTER TIME IN ORDER TO CALCULATE THE THEORETICAL PROBABILITY."
3170  PRINT "WOULD YOU LIKE TO CONTINUE WITH THIS EXPERIMENT OR TRY"
3180  PRINT "A NEW EXPERIMENT?  TYPE (CONTINUE OR NEW).";
3190  INPUT G$
3200  PRINT 
3210  IF G$="NEW" THEN 730
3220  IF G$="CONTINUE" THEN 3260
3230  GOSUB 5420
3240  GOTO 3170
3250  PRINT "THERE WILL BE A PAUSE FOR CALCULATIONS."
3260  IF N9=-5 THEN 4530
3270  IF N9=0 THEN 4500
3280  IF Z1=4 THEN 4530
3290  IF C2=2 OR C2=6 THEN 3320
3300  GOSUB 3780
3310  GOTO 3330
3320  GOSUB 3750
3330  PRINT "IF YOU DO NOT KNOW THE ANSWER TO THE NEXT QUESTION, TYPE 9."
3340  C6=0
3350  PRINT "***WHAT IS THE THEORETICAL PROBABILITY";
3360  INPUT P5
3370  PRINT 
3380  IF P5=9 THEN 3430
3390  IF ABS(P5-(M5/N5)) <= .005 THEN 3660
3400  X5=X5+1
3410  IF C6#0 THEN 3520
3420  C6=C6+1
3430  PRINT "IN ORDER TO HELP YOU ANSWER THE ABOVE QUESTION CORRECTLY"
3440  PRINT "THE SAMPLE SPACE WILL BE PRINTED.  COUNT HOW MANY TIMES YOUR""PARTICULAR EVENT OCCURS."
3450  PRINT 
3460  A5=2
3470  IF S5=100 THEN 3500
3480  GOSUB 3750
3490  GOTO 3520
3500  GOSUB 3780
3510  IF P5=9 THEN 3590
3520  PRINT "DO YOU WANT TO CALCULATE THE THEORETICAL PROBABILITY AGAIN";
3530  INPUT A$
3540  PRINT 
3550  IF A$="YES" THEN 3350
3560  IF A$="NO" THEN 3590
3570  GOSUB 5420
3580  GOTO 3520
3590  PRINT "DO YOU WANT THE CORRECT THEORETICAL PROBABILITY PRINTED";
3600  INPUT A$
3610  PRINT 
3620  IF A$="NO" THEN 3680
3630  IF A$="YES" THEN 5490
3640  GOSUB 5420
3650  GOTO 3590
3660  PRINT "GOOD!  THAT IS THE CORRECT THEORETICAL PROBABILITY."
3670  PRINT 
3680  PRINT "DO YOU WANT TO TRY ANOTHER EXPERIMENT";
3690  INPUT A$
3700  PRINT 
3710  IF A$="NO" THEN 5460
3720  IF A$="YES" THEN 680
3730  GOSUB 5420
3740  GOTO 3660
3750  FOR I=1 TO N1
3760  S[I]=S5
3770  NEXT I
3780  T=N1
3790  GOTO T OF 3840,3830,3820,3810,3800
3800  FOR A=1 TO S[I-5]
3810  FOR B=1 TO S[I-4]
3820  FOR C=1 TO S[I-3]
3830  FOR D=1 TO S[I-2]
3840  FOR E=1 TO S[I-1]
3850  IF A5=2 THEN 3870
3860  GOTO T OF 4140,4080,4020,3960,3900
3870  GOTO T OF 4110,4050,3990,3930,3880
3880  PRINT A;B;C;D;E
3890  GOTO 4190
3900  N5=N5+1
3910  IF A+B+C+D+E=N3 THEN 4170
3920  GOTO 4270
3930  F=1
3940  PRINT B;C;D;E
3950  GOTO 4190
3960  N5=N5+1
3970  IF B+C+D+E=N3 THEN 4170
3980  GOTO 4270
3990  F=G=1
4000  PRINT C;D;E
4010  GOTO 4190
4020  N5=N5+1
4030  IF C+D+E=N3 THEN 4170
4040  GOTO 4270
4050  F=G=H=1
4060  PRINT D;E
4070  GOTO 4190
4080  N5=N5+1
4090  IF D+E=N3 THEN 4170
4100  GOTO 4270
4110  F=G=H=I=1
4120  PRINT E
4130  GOTO 4190
4140  N5=N5+1
4150  IF E=N3 THEN 4170
4160  GOTO 4270
4170  M5=M5+1
4180  GOTO 4270
4190  U7=U7+1
4200  IF U7/10#INT(U7/10) THEN 4270
4210  PRINT "     DO YOU WANT MORE OF THE SAMPLE SPACE";
4220  INPUT A$
4230  IF A$="YES" THEN 4270
4240  IF A$="NO" THEN 4320
4250  GOSUB 5420
4260  GOTO 4210
4270  NEXT E
4280  NEXT D
4290  NEXT C
4300  NEXT B
4310  NEXT A
4320  PRINT 
4330  U7=0
4340  RETURN 
4350  A9=240
4360  PRINT "THE FIRST SUM FOR THE DOWN SIDES = ";
4370  ENTER A9,B9,N3
4380  PRINT '13
4390  IF B9=-256 THEN 4470
4400  PRINT "THE SECOND SUM FOR THE DOWN SIDES = ";
4410  ENTER A9,B9,N9
4420  PRINT '13
4430  IF B9=-256 THEN 4470
4440  PRINT 
4450  PRINT 
4460  GOTO 1490
4470  PRINT "TAKE YOUR TIME.  TYPE YOUR ANSWER WHEN YOU HAVE IT."
4480  PRINT 
4490  GOTO 4360
4500  N3=N8
4510  N9=-5
4520  GOTO 2070
4530  PRINT "NOW YOU HAVE FOUND THE FOLLOWING PROBABILITIES."'10
4540  PRINT TAB(5);"P(A)="P[1];TAB(35);"P(B)="P[2]
4550  PRINT TAB(5);"P(A UNION B)="P[3];TAB(35);"P(A&B)="P[4]
4560  PRINT 
4570  PRINT "CAN YOU SEE WHAT THE FORMULA IS NOW";
4580  INPUT A$
4590  PRINT 
4600  IF A$="NO" THEN 6150
4610  IF A$="YES" THEN 4640
4620  GOSUB 5420
4630  GOTO 4570
4640  IF Z2=3 THEN 5140
4650  IF Z2=1 THEN 5980
4660  PRINT "THE CORRECT FORMULA FOR THE P(A UNION B) IS";
4670  INPUT C$
4680  PRINT 
4690  IF Z2=2 THEN 5000
4700  PRINT 
4710  GOTO 6030
4720  PRINT "GOOD!  YOU HAVE DISCOVERED AN IMPORTANT PROBABILITY THEOREM."
4730  PRINT 
4740  PRINT "THEOREM - IF 'A' AND 'B' ARE MUTUALLY EXCLUSIVE"
4750  PRINT "          EVENTS THEN THE P(A UNION B)=P(A)+P(B)"
4760  PRINT 
4770  PRINT "DO YOU WANT TO TRY SOME OTHER FORMULAS";
4780  Z2=2
4790  INPUT A$
4800  PRINT 
4810  IF A$="NO" THEN 5460
4820  IF A$="YES" THEN 6300
4830  GOSUB 5420
4840  GOTO 4770
4850  PRINT "THE OUTCOME FOR THE FIRST POLYHEDRON IS";
4860  INPUT N3
4870  PRINT 
4880  PRINT "THE OUTCOME FOR THE SECOND POLYHEDRON IS";
4890  INPUT N9
4900  PRINT 
4910  GOTO 1490
4920  N9=N5
4930  N5=N3
4940  N3=0
4950  Z1=40
4960  GOTO 2070
4970  PRINT "USING NO SPACES COMPLETE THE FORMULA FOR P(A&B) ";
4980  N3=N5
4990  GOTO 2070
5000  IF C$=F$[6,21] THEN 5070
5010  IF C$=F$[1,16] THEN 5070
5020  IF C$=F$[23,38] THEN 5070
5030  IF C$=F$[28,43] THEN 5070
5040  IF C$=F$[10,26] THEN 5070
5050  IF C$=F$[32,48] THEN 5070
5060  GOTO 6150
5070  PRINT "THAT'S ANOTHER PROBABILITY THEOREM."
5080  PRINT 
5090  PRINT "THEOREM - IF 'A' AND 'B' ARE EVENTS IN A FINITE SAMPLE SPACE"
5100  PRINT "          THEN THE P(A UNION B) = P(A)+P(B)-P(A&B)"
5110  PRINT 
5120  PRINT "NOW LET'S TRY TO COMPLETE ONE MORE FORMULA DEALING"
5130  PRINT "WITH THE PROBABILITY OF THE INTERSECTION OF 2 EVENTS"
5140  PRINT "WITH THE PROBABILITY OF THE INTERSECTION OF 2 EVENTS."
5150  PRINT "(USE NO SPACES WHEN TYPING YOUR FORMULA.)"
5160  INPUT C$
5170  Z2=3
5180  PRINT 
5190  IF C$=F$[45,53] THEN 5220
5200  IF C$=F$[50,58] THEN 5220
5210  GOTO 6150
5220  PRINT "GREAT -- YOU HAVE JUST COME UP WITH THE BASIC IDEA "
5230  PRINT "FOR INDEPENDENT EVENTS."
5240  PRINT 
5250  PRINT "INDEPENDENT EVENTS ARE EVENTS THAT HAVE NOTHING TO"
5260  PRINT "TO DO WITH EACH OTHER."
5270  PRINT 
5280  PRINT "DEFINITION - EVENTS 'A' AND 'B' ARE INDEPENDENT"
5290  PRINT "             IF AND ONLY IF P(A&B)=P(A)*P(B)"
5300  PRINT 
5310  PRINT "DO YOU WANT TO DO SOME MORE EXAMPLES OF THIS TYPE";
5320  INPUT A$
5330  IF A$="NO" THEN 6500
5340  IF A$="YES" THEN 5380
5350  GOSUB 5420
5360  GOTO 5310
5370  GOTO 1080
5380  PRINT 
5390  PRINT "THIS EXPERIMENT WILL DEAL WITH 2 DISTINGUISHABLE POLYHEDRA."'10
5400  W5=5
5410  GOTO 1080
5420  PRINT 
5430  PRINT "YOU HAVE MADE A TYPING MISTAKE.  TRY AGAIN!"
5440  PRINT 
5450  RETURN 
5460  PRINT "YOU SHOULD NOW SEE SOME DIFFERENCE BETWEEN THEORETICAL AND""EXPERIMENTAL PROBABILITY."
5470  PRINT 
5480  GOTO 6520
5490  PRINT "THE CORRECT THEORETICAL PROBABILITY IS "M5/N5
5500  PRINT 
5510  GOTO 3680
5520  IF N1=1 OR N1=2 OR N1=3 OR N1=4 OR N1=5 THEN 5550
5530  PRINT 
5540  PRINT "YOU HAVE INPUT AN INCORRECT NUMBER OF THROWS OR"
5550  RETURN 
5560  Z2=0
5570  PRINT "DO YOU WANT INSTRUCTIONS FOR RUNNING UNION";
5580  INPUT A$
5590  PRINT 
5600  IF A$="YES" THEN 5640
5610  IF A$="NO" THEN 5970
5620  GOSUB 5420
5630  GOTO 5570
5640  PRINT "TRY TO COMPLETE THE FOLLOWING PROBABILITY FORMULAS,"
5650  PRINT "USING EXPERIMENTAL PROBABILITIES:"
5660  PRINT 
5670  PRINT "FOR EXAMPLE IF ASKED TO COMPLETE THIS FORMULA:"
5680  PRINT "     P(A UNION B) ="
5690  PRINT "AN INCORRECT RESPONSE MIGHT BE   P(B) * P(A)."
5700  PRINT 
5710  PRINT "IF YOU CANNOT ANSWER ONE OF THE QUESTIONS, TYPE NO."
5720  PRINT 
5730  PRINT "THE SYMBOL FOR INTERSECTION WILL BE &.  THE PROBABILITY"
5740  PRINT "FOR 'A' INTERSECTION 'B' WILL BE WRITTEN P(A&B)."
5750  PRINT "WHEN YOU ARE TYPING A COMPLETED FORMULA DON'T USE ANY SPACES."
5760  PRINT 
5770  PRINT "ALL THE COMPLETED FORMULAS WILL USE SOME COMBINATION OF"
5780  PRINT "P(A&B),P(A UNION B),P(A),AND P(B)."
5790  PRINT 
5800  PRINT "----- DEFINITION:"
5810  PRINT "IF 2 EVENTS CANNOT HAPPEN AT THE SAME TIME, THEY ARE SAID TO BE"
5820  PRINT "MUTUALLY EXCLUSIVE."
5830  PRINT 
5840  PRINT "     EXAMPLE 1 - TWO COINS ARE TOSSED.  EVENT 'A' IS"
5850  PRINT "     'GETTING 2 HEADS', AND EVENT 'B' IS 'GETTING 2 TAILS'."
5860  PRINT "     EVENTS 'A' AND 'B' ARE MUTUALLY EXCLUSIVE, AND"
5870  PRINT "     'A' INTERSECTION 'B' = EMPTY SET."
5880  PRINT 
5890  PRINT "     EXAMPLE 2 - A DIE IS ROLLED.  EVENT 'A' IS 'GETTING"
5900  PRINT "     A PRIME NUMBER' (2,3,5), AND EVENT 'B' IS 'GETTING"
5910  PRINT "     AN EVEN NUMBER' (2,4,6).  EVENTS 'A' AND 'B' ARE NOT"
5920  PRINT "     MUTUALLY EXCLUSIVE SINCE THERE IS A COMMON ELEMENT (2)"
5930  PRINT "     IN THEIR SAMPLE SPACES."
5940  PRINT 
5950  PRINT "NOW TRY TO COMPLETE THESE PROBABILITY FORMULAS:"
5960  PRINT 
5970  PRINT "COMPLETE THE FOLLOWING:"
5980  PRINT "IF 2 EVENTS 'A' AND 'B' ARE MUTUALLY EXCLUSIVE"
5990  PRINT "   P(A UNION B) =";
6000  INPUT C$
6010  PRINT 
6020  Z2=1
6030  IF C$=F$[1,9] THEN 4720
6040  IF C$=F$[40,48] THEN 4720
6050  GOTO 6150
6060  PRINT "DO YOU WANT TO WRITE THE FORMULA AGAIN";
6070  INPUT A$
6080  PRINT 
6090  IF A$="NO" THEN 6500
6100  IF A$="YES" THEN 6130
6110  GOSUB 5420
6120  GOTO 6150
6130  IF R9=5 THEN 6330
6140  GOTO 5980
6150  PRINT "DO YOU WANT TO DO AN EXPERIMENT "
6160  PRINT "TO HELP YOU DISCOVER THE CORRECT FORMULA";
6170  INPUT A$
6180  PRINT 
6190  IF A$="NO" THEN 6500
6200  IF A$="YES" THEN 6230
6210  GOSUB 5420
6220  GOTO 6150
6230  IF R9=5 OR Z2=2 THEN 6440
6240  PRINT '10"----- TOSSING POLYHEDRA:"
6250  PRINT "DESIGN THE EXPERIMENT: THE NUMBER OF POLYHEDRA (MAXIMUM OF 5),"
6260  PRINT "EVENT 'A' (ONE SUM FOR THE DOWN SIDES), AND EVENT 'B'"
6270  PRINT "(A SECOND SUM FOR THE DOWN SIDES)."
6280  PRINT 
6290  GOTO 1020
6300  PRINT "NOW LET'S SEE IF YOU CAN DISCOVER ANOTHER FORMULA."
6310  PRINT 
6320  PRINT "COMPLETE THE FOLLOWING:"
6330  PRINT "IF A AND B ARE EVENTS IN A FINITE SAMPLE SPACE AND "
6340  PRINT "'A' AND 'B' ARE NOT NECESSARILY MUTUALLY EXCLUSIVE"
6350  PRINT "   P(A UNION B) = ";
6360  INPUT C$
6370  PRINT 
6380  Z2=2
6390  O=1
6400  R9=5
6410  IF C$="NO" THEN 6150
6420  GOTO 5000
6430  PRINT 
6440  PRINT '10"----- TOSSING 2 DISTINGUISHABLE POLYHEDRA:"
6450  PRINT "DESIGN THE EXPERIMENT: EVENT 'A' (THE OUTCOME FOR THE FIRST"
6460  PRINT "POLYHEDRON), AND EVENT 'B' (THE OUTCOME FOR THE SECOND POLYHEDRON)."
6470  N1=2
6480  GOTO 1080
6490  PRINT 
6500  PRINT 
6510  PRINT "SINCE YOU DID NOT GET THE CORRECT FORMULA ANALYZE YOUR DATA AND""TRY AGAIN.  SOMETIME SOON."
6520  END 
