10 REM PROGRAM NAME = CONDI, CONDITIONAL PROBABILITY 20 DIM A$[3],B$[30] 30 Z1=2 40 PRINT "DO YOU WANT INSTRUCTIONS FOR RUNNING CONDI "; 50 INPUT A$ 60 IF A$="YES" THEN 100 70 IF A$="NO" THEN 340 80 GOTO 40 90 PRINT "----- DEFINITION:" 100 PRINT "CONDITIONAL PROBABILITY DEALS WITH A REDUCED SAMPLE SPACE." 110 PRINT " EXAMPLE: TWO 3'S AND TWO 5'S ARE ARRANGED IN SOME ORDER." 120 PRINT " ALL ARRANGEMENTS ARE EQUALLY LIKELY." 130 PRINT " IF THE LAST NUMBER IN THE ARRANGEMENT IS A 5," 140 PRINT " WHAT IS THE PROBABILITY THAT THE TWO 3'S ARE TOGETHER?" 150 PRINT 160 PRINT " SAMPLE SAPCE OF THE POSSIBLE ARRANGEMENTS:" 170 PRINT " (3,3,5,5), (3,5,3,5), (3,5,5,3), (5,3,5,3), (5,5,3,3), (5,3,3,5)" 180 PRINT 190 PRINT " A REDUCED SAMPLE SPACE WITH A 5 AS THE LAST ELEMENT IS" 200 PRINT " (3,3,5,5), (3,5,3,5), (5,3,3,5)" 210 PRINT 220 PRINT " EVENT 'A' IS 'THE TWO E'S ARE TOGETHER'." 230 PRINT " SINCE THERE ARE TWO SAMPLE POINTS IN 'A'," 240 PRINT " P(A) = 2/3." 250 PRINT 260 PRINT "IS THERE AN EQUATION FOR CALCULATING CONDITIONAL PROBABILITIES?" 270 PRINT 280 PRINT "TRY THE FOLLOWING EXPERIMENT - TOSSING UP TO 5 POLYHEDRA:" 290 PRINT "EVENT 'A' IS 'AT LEAST ONE POLYHEDRON WILL STOP WITH A SIDE" 300 PRINT "DOWN OF YOUR CHOICE'. EVENT 'B' IS 'THE SUM OF THE DOWN SIDES" 310 PRINT "IS LESS THAN A SUM OF YOUR CHOICE'." 320 PRINT 330 PRINT "IT WILL BE HELPFUL TO HAVE THE SAMPLE SPACE PRINTED FOR YOU." 340 N5=X5=M[1]=M[2]=M[3]=C8=N6=0 350 PRINT 360 PRINT 370 A5=A4=A3=A2=A1=0 380 PRINT "HOW MANY POLYHEDRA DO YOU WANT TO TOSS (MAXIMUM OF 5)"; 390 INPUT N1 400 PRINT 410 IF INT(N1)=N1 AND N1<6 AND N1 >= 1 THEN 440 420 PRINT "YOU HAVE INPUT AN INCORRECT NUMBER OF POLYHEDRA."'10 430 GOTO 380 440 E1=1 450 FOR L2=1 TO 5 460 S[L2]=1 470 NEXT L2 480 PRINT "HOW MANY SIDES FOR EACH POLYHEDRON:" 490 PRINT "TYPE ONE NUMBER AND THE RETURN KEY FOR EACH QUESTION MARK." 500 PRINT 510 FOR I=1 TO N1 520 INPUT S[I] 530 N6=N6+S[I] 540 IF INT(S[I])=S[I] AND S[I]>1 THEN 570 550 PRINT "YOU HAVE INPUT AN INCORRECT NUMBER OF SIDES FOR YOUR POLYHEDRON." 560 GOTO 480 570 NEXT I 580 PRINT 590 PRINT "EVENT 'B', THE SUM OF THE DOWN SIDES IS LESS THAN "; 600 INPUT N3 610 IF N3 >= N1 AND N3 <= N6 THEN 640 620 GOSUB 2530 630 GOTO 590 640 PRINT 650 PRINT "EVENT 'A', AT LEAST ONE POLYHEDRON WILL HAVE THIS SIDE DOWN "; 660 INPUT N2 670 FOR I=1 TO N1 680 IF N2>0 AND N2 <= S[I] THEN 720 690 NEXT I 700 GOSUB 2530 710 GOTO 650 720 PRINT 730 PRINT "DO YOU WANT THE SAMPLE SPACE PRINTED"; 740 INPUT A$ 750 PRINT 760 IF A$="YES" THEN 800 770 IF A$="NO" THEN 820 780 GOSUB 2070 790 GOTO 730 800 X1=1 810 GOSUB 2100 820 GOSUB 2090 830 P[1]=M[2]/N5 840 P[2]=M[1]/N5 850 P[3]=M[3]/N5 860 IF M[1]=0 THEN 2530 870 P[4]=N5/M[1]*M[3]/N5 880 PRINT "NOW, CALCULATE THE FOLLOWING PROBABILITIES:" 890 PRINT 900 PRINT "1.P(A) 2.P(B) 3.P(A&B) 4. P(A GIVEN B) " 910 PRINT 920 FOR L=1 TO 4 930 PRINT L'13TAB(2)".?"; 940 A9=240 950 ENTER A9,B9,P 960 IF P <= 1 AND P >= 0 THEN 1000 970 PRINT 980 PRINT "ALL PROBABILITIES MUST BE BETWEEN 0 AND 1 INCLUSIVE. TRY AGAIN!" 990 GOTO 930 1000 GOSUB 1890 1010 IF Q=0 THEN 1370 1020 INPUT A$ 1030 PRINT 1040 IF A$="YES" THEN 930 1050 IF A$="NO" THEN 1080 1060 GOSUB 2070 1070 GOSUB 1920 1080 PRINT "DO YOU WANT THE SAMPLE SPACE PRINTED"; 1090 INPUT A$ 1100 PRINT 1110 IF A$="NO" THEN 1200 1120 IF A$="YES" THEN 1150 1130 GOSUB 2070 1140 GOTO 1080 1150 X1=1 1160 GOSUB 2100 1170 PRINT "NOW, CALCULATE THE PROBABILITY." 1180 PRINT 1190 GOTO 930 1200 PRINT "DO YOU WANT THE CORRECT PROBABILITY PRINTED "; 1210 INPUT A$ 1220 PRINT 1230 IF A$="NO" THEN 2550 1240 IF A$="YES" THEN 1270 1250 GOSUB 2070 1260 GOTO 1200 1270 PRINT "THE CORRECT PROBABILITY IS "P[L] 1280 PRINT 1290 C8=C8+1 1300 PRINT "DO YOU WANT TO CONTINUE"; 1310 INPUT A$ 1320 PRINT 1330 IF A$="YES" THEN 1370 1340 IF A$="NO" THEN 2550 1350 GOSUB 2070 1360 GOTO 1300 1370 NEXT L 1380 FOR J=1 TO 3 1390 N=N5 1400 M=M[J] 1410 GOSUB 1990 1420 M[J]=M 1430 N[J]=N 1440 NEXT J 1450 N=N5*M[8] 1460 M=N5*M[9] 1470 GOSUB 1990 1480 M[4]=M 1490 N[4]=N 1500 IF C8>2 THEN 1520 1510 PRINT "YOU CORRECTLY CALCULATED"4-C8" OF THE PROBABILITIES." 1520 PRINT "THE PROBABILITIES COULD HAVE BEEN WRITTEN IN THE FOLLOWING WAY." 1530 PRINT 1540 PRINT "1. P(A) = "M[2]"/"N[2] 1550 PRINT "2. P(B) = "M[1]"/"N[1] 1560 PRINT "3. P(A&B) = "M[3]"/"N[3] 1570 PRINT "4. P(A GIVEN B) = "M[4]"/"N[4] 1580 PRINT 1590 PRINT "CAN YOU SEE WHAT THE FORMULA FOR THE PROBABILITY OF 'A' GIVEN 'B'" 1600 PRINT "WOULD BE USING SOME COMBINATION OF P(A&B) AND P(B)"; 1610 INPUT A$ 1620 PRINT 1630 IF A$="YES" THEN 1720 1640 IF A$="NO" THEN 1670 1650 GOSUB 2070 1660 GOTO 1590 1670 PRINT "DO YOU WANT TO TRY ANOTHER EXPERIMENT"; 1680 INPUT A$ 1690 PRINT 1700 IF A$="NO" THEN 2550 1710 IF A$="YES" THEN 340 1720 PRINT "COMPLETE THE FOLLOWING:" 1730 PRINT " P(A GIVEN B) = "; 1740 INPUT B$ 1750 IF B$="P(A&B)/P(B)" THEN 1840 1760 IF B$="P(B&A)/P(B)" THEN 1840 1770 PRINT "NOT QUITE! DO YOU WANT TO TRY AGAIN"; 1780 INPUT A$ 1790 PRINT 1800 IF A$="YES" THEN 1720 1810 IF A$="NO" THEN 1670 1820 GOSUB 2070 1830 GOTO 1720 1840 PRINT 1850 PRINT "THAT IS THE FORMULA FOR CONDITIONAL PROBABILITY!" 1860 PRINT "DEFINITION -- THE CONDITIONAL PROBABILITY OF AN EVENT A, GIVEN B,""IS DEFINED BY P(A GIVEN B) = P(A&B)/P(B)" 1870 PRINT "IS DEFINED BY THE EQUATION P(A GIVEN B)=P(A&B)/P(B), IF P(B)#0." 1880 GOTO 2570 1890 IF ABS(P-P[L])<.001 THEN 1950 1900 PRINT 1910 PRINT 1920 PRINT "THAT IS NOT CORRECT. DO YOU WANT TO TRY AGAIN "; 1930 Q=1 1940 GOTO 1980 1950 Q=0 1960 PRINT '13;TAB(12);"CORRECT!" 1970 PRINT 1980 RETURN 1990 FOR K=2 TO M 2000 IF M/K=INT(M/K) AND N/K=INT(N/K) THEN 2020 2010 GOTO 2050 2020 M=M/K 2030 N=N/K 2040 GOTO 2000 2050 NEXT K 2060 RETURN 2070 PRINT "YOU HAVE MADE A TYPING MISTAKE. TRY AGAIN!" 2080 RETURN 2090 X1=N5=0 2100 U7=0 2110 GOTO N1 OF 2160,2150,2140,2130,2120 2120 FOR A5=1 TO S[L2-1] 2130 FOR A4=1 TO S[L2-2] 2140 FOR A3=1 TO S[L2-3] 2150 FOR A2=1 TO S[L2-4] 2160 FOR A1=1 TO S[L2-5] 2170 IF X1=0 THEN 2260 2180 U7=U7+1 2190 GOTO N1 OF 2240,2230,2220,2210,2200 2200 PRINT A5; 2210 PRINT A4; 2220 PRINT A3; 2230 PRINT A2; 2240 PRINT A1 2250 GOTO 2360 2260 N5=N5+1 2270 A9=A1+A2+A3+A4+A5 2280 IF A9 >= N3 THEN 2300 2290 M[1]=M[1]+1 2300 IF A1=N2 OR A2=N2 OR A3=N2 OR A4=N2 OR A5=N2 THEN 2320 2310 GOTO 2430 2320 M[2]=M[2]+1 2330 IF A9 >= N3 THEN 2430 2340 M[3]=M[3]+1 2350 GOTO 2430 2360 IF U7/10#INT(U7/10) THEN 2430 2370 PRINT "DO YOU WANT MORE OF THE SAMPLE SPACE "; 2380 INPUT A$ 2390 IF A$="YES" THEN 2430 2400 IF A$="NO" THEN 2510 2410 GOSUB 2070 2420 GOTO 2360 2430 NEXT A1 2440 NEXT A2 2450 NEXT A3 2460 NEXT A4 2470 NEXT A5 2480 IF X1=1 THEN 2510 2490 M[8]=M[1] 2500 M[9]=M[3] 2510 PRINT 2520 RETURN 2530 PRINT '10"YOU HAVE INPUT AN INCORRECT VALUE FOR YOUR EVENT. CHECK THE NUMBER""OF POLYHEDRA YOU ARE THROWING AND THE NUMBER OF SIDES."'10 2540 RETURN 2550 PRINT "SINCE YOU DID NOT GET THE CORRECT RELATIONSHIP." 2560 PRINT "ANALYZE YOUR DATA AND TRY AGAIN." 2570 END