10  COM Z1,M4,N4,T1,S1,F1,S2,P8,P9,Q8,Y1
20  GOTO 60
30  CHAIN "$PASCL"
40  REM PROGRAM NAME = BINOM, BINOMIAL EXPERIMENTS AND
50  REM  THE BINOMIAL PROBABILITY DISTRIBUTION
60  DIM A$[3],E$[3],F$[3],B$[10],G$[10],H$[10],C$[10],J$[10]
70  DIM K$[50],L$[50]
80  DIM A[130,7]
90  U1=0
100  IF Z1=10 THEN 570
110  PRINT "DO YOU WANT INSTRUCTIONS FOR RUNNING BINOM";
120  INPUT A$
130  PRINT 
140  IF A$="YES" THEN 170
150  IF A$="NO" THEN 560
160  GOTO 110
170  U1=5
180  PRINT "THIS PROGRAM INVESTIGATES BINOMIAL EXPERIMENTS AND"
190  PRINT "BINOMIAL PROBABILITY DISTRIBUTION."
200  PRINT '10"----- DEFINITION:"
210  PRINT "BINOMIAL EXPERIMENTS ARE COMPOSED OF REPETITIONS OF INDEPENDENT"
220  PRINT "TRIALS, EACH WITH 2 POSSIBLE OUTCOMES.  THE 2 POSSIBLE OUTCOMES"
230  PRINT "ARE USUALLY CALLED SUCCESS AND FAILURE."
240  PRINT 
250  PRINT "----- DEFINITION:  BINOMIAL PROBABILITY DISTRIBUTION -"
260  PRINT "AN EXPERIMENT CONSISTS OF 'N' INDEPENDENT BINOMIAL TRIALS."
270  PRINT "EACH TRIAL HAS PROBABILITY P OF SUCCESS AND PROBABILITY Q"
280  PRINT "(Q = 1 - P) OF FAILURE.  THE BINOMIAL PROBABILITY DISTRIBUTION"
290  PRINT "IS ALL OF THE PROBABILITIES OF EXACTLY 'X' SUCCESSES AND"
300  PRINT "'N-X' FAILURES (X = 1,2,3...N).  THE SUM OF THESE PROBABILITIES IS 1."
310  PRINT 
320  PRINT "----- DESIGN AN EXPERIMENT:"
330  PRINT "      1) THE NUMBER OF TOSSES, N, FOR THE POLYHEDRON FOR ONE "
340  PRINT "         EXPERIMENT."
350  PRINT "      2) THE NUMBER OF SIDES ON THE POLYHEDRON."
360  PRINT "      3) THE SUCCESS - THE SIDE OR SIDES WHICH YOU WANT DOWN."
370  PRINT "      4) THE NUMBER OF SUCCESSES, X, FOR ONE EXPERIMENT."
380  PRINT "THEN YOUR CALCULATION FOR P(EXACTLY X SUCCESSES AND N-X FAILURES)."
390  PRINT "      EXAMPLE EXPERIMENTAL DESIGN:"
400  PRINT "      1) TOSS A POLYHEDRON 3 TIMES."
410  PRINT "      2) 6 SIDES ON THE POLYHEDRON - LIKE A DIE."
420  PRINT "      3) SUCCESS - THE 2 OR THE 5 ON THE DOWN SIDE."
430  PRINT "         P(SUCCESS - A 2 OR A 5) = 2/6 = 1/3, SINCE THERE ARE"
440  PRINT "         2 WAYS FOR SUCCESS OUT OF 6 POSSIBLE OUTCOMES."
450  PRINT "         P(FAILURE) = 4/6 = 2/3.  P(SUCCESS) + P(FAILURE) = 1."
460  PRINT "      4) WE DESIRE 2 SUCCESS IN THE 3 TOSSES.  THE 2 SUCCESSES AND"
470  PRINT "         1 FAILURE MAY OCCUR IN 3 DIFFERENT WAYS: SSF, SFS, FSS."
480  PRINT "      5) CALCULATE P(2 SUCCESSES AND 1 FAILURE):"
490  PRINT "         P(SUCCESS) = 1/3"
500  PRINT "         P(FAILURE) = 2/3"
510  PRINT "         P(SUCCESS AND FAILURE) = P(SUCCESS) * P(FAILURE) = 2/9"
520  PRINT "         SINCE (2 SUCCESS AND 1 FAILURE) CAN OCCUR IN 3 WAYS,"
530  PRINT "         P(2 SUCCESSES AND 1 FAILURE) = 2/9 + 2/9 + 2/9 = 2/3."
540  PRINT 
550  PRINT "NOW TRY YOUR OWN EXPERIMENT."
560  C1=M2=M4=N4=C7=0
570  B$='10"CORRECT!"
580  C$="RIGHT!"
590  G$="SUCCESSES"
600  H$="FAILURES"
610  J$=" TOSSES"
620  E$="NO"
630  F$="YES"
640  L$="R*P^X*Q^(N-X)*R*Q^(N-X)*P^X*R*Q^(N-X)*R*P^X"
650  IF Z1=10 THEN 3050
660  PRINT '10"----- DESIGN THE EXPERIMENT:"'10
670  PRINT "-- 1) HOW MANY TOSSES OF THE POLYHEDRON (MAXIMUM OF 7)";
690  INPUT T1
700  IF T1 <= 7 AND T1 >= 1 AND T1=INT(T1) THEN 730
710  GOSUB 3860
720  GOTO 670
725  PRINT 
730  PRINT "-- 2) HOW MANY SIDES ON THE POLYHEDRON";
740  INPUT S1
750  IF INT(S1)=S1 AND S1>1 THEN 780
760  GOSUB 3860
770  GOTO 730
780  PRINT "-- 3) SUCCESS:  A) HOW MANY DIFFERENT SIDES";
790  INPUT F1
800  PRINT '13;
810  IF INT(F1)=F1 AND F1 <= S1 THEN 840
820  GOSUB 3860
830  GOTO 780
840  PRINT "-- 3) SUCCESS:  B) WHICH SIDES?"
850  PRINT "      (TYPE ONE NUMBER AND THE RETURN KEY FOR EACH QUESTION MARK)"
870  FOR H=1 TO F1
875  PRINT "      ";
880  INPUT B[H]
890  IF B[H]>0 AND B[H] <= S1 AND B[H]=INT(B[H]) THEN 920
900  GOSUB 3860
910  GOTO 880
920  NEXT H
930  PRINT "-- 4) HOW MANY SUCCESSES OUT OF"T1;
940  PRINT " DO YOU WANT";
950  INPUT S2
960  PRINT 
970  IF S2 >= 1 AND S2 <= T1 AND S2=INT(S2) THEN 1000
980  GOSUB 3860
990  GOTO 930
1000  PRINT "SINCE YOU HAVE "S2;
1010  GOSUB 4110
1020  PRINT " THEN YOU MUST HAVE "T1-S2;
1030  GOSUB 4160
1040  PRINT "."
1050  C1=C1+1
1060  IF C1#1 THEN 1120
1070  IF U1=0 THEN 1120
1080  PRINT "-- 5) THE PROBABILITIES: (AS FRACTIONS)"
1090  PRINT "      TYPE THE NUMERATOR AND DENOMINATOR SEPARATELY, THE NUMERATOR"
1100  PRINT "      FIRST (THEN THE RETURN KEY), THEN THE DENOMINATOR (RETURN)."
1110  PRINT 
1120  PRINT "      IF YOU DO NOT KNOW AN ANSWER, TYPE 999."
1130  GOTO 1150
1140  PRINT "      RETURNING,"
1150  PRINT '10"WHAT IS THE PROBABILITY OF EXACTLY"S2
1160  GOSUB 4110
1170  PRINT " OUT OF "T1;
1180  GOSUB 4210
1190  PRINT "?"
1200  GOSUB 3670
1210  GOSUB 3490
1220  P8=(F1/S1)^S2
1230  Q8=((S1-F1)/S1)^(T1-S2)
1240  P9=Y1*P8*Q8
1250  IF ABS(P-P9)<.001 THEN 3240
1260  IF M4=100 THEN 1300
1270  IF M4=50 THEN 3430
1280  IF M4#0 THEN 3330
1290  GOTO 1310
1300  PRINT "THE PROBABILITY IS"V5"/"V6
1310  PRINT "WHAT IS THE PROBABILITY OF ONE TOSS BEING A SUCCESS?"
1320  GOSUB 3670
1330  IF ABS(P-F1/S1)<.001 THEN 1440
1340  PRINT '10"SINCE THE POLYHEDRON HAS"S1"SIDES AND THERE"
1350  IF F1=1 THEN 1380
1360  PRINT " ARE "F1"WAYS IN WHICH YOU CAN GET A SUCCESS."
1370  GOTO 1390
1380  PRINT " IS 1 WAY IN WHICH YOU CAN GET A SUCCESS."
1390  PRINT "THE PROBABILITY IS";
1400  V5=F1
1410  V6=S1
1420  GOSUB 4310
1430  GOTO 1460
1440  PRINT B$
1450  IF S2=1 THEN 1670
1460  PRINT '10"WHAT IS THE PROBABILITY OF EXACTLY"
1470  PRINT S2;
1480  GOSUB 4210
1490  PRINT " BEING ";
1500  GOSUB 4110
1510  PRINT "?"
1520  GOSUB 3670
1530  IF ABS(P-(F1/S1)^S2)<.001 THEN 1660
1540  C7=C7+1
1550  IF C7=1 THEN 1630
1560  GOSUB 4390
1570  IF C8=1 THEN 1460
1580  PRINT "THE ANSWER IS";
1590  V5=F1^S2
1600  V6=S1^S2
1610  GOSUB 4310
1620  GOTO 1650
1630  GOSUB 3900
1640  GOTO 1460
1650  C7=0
1660  PRINT B$
1670  PRINT "IF P(SUCCESS) ="F1"/"S1", WHAT IS P(FAILURE)?";
1680  GOSUB 3670
1690  IF ABS(P-(S1-F1)/S1)<.001 THEN 1720
1700  PRINT '10"P(SUCCESS)+P(FAILURE)= 1.  TRY AGAIN!"
1710  GOTO 1670
1720  PRINT C$
1730  IF T1-S2=1 THEN 1940
1740  PRINT '10"WHAT IS THE PROBABILITY OF THE LAST"T1-S2
1750  GOSUB 4260
1760  PRINT " BEING ";
1770  GOSUB 4160
1780  PRINT "?"
1790  GOSUB 3670
1800  IF ABS(P-Q8)<.001 THEN 1920
1810  C7=C7+1
1820  IF C7=1 THEN 1900
1830  GOSUB 4390
1840  IF C8=1 THEN 1740
1850  PRINT "THE ANSWER IS";
1860  V5=(S1-F1)^(T1-S2)
1870  V6=S1^(T1-S2)
1880  GOSUB 4310
1890  GOTO 1930
1900  GOSUB 3900
1910  GOTO 1740
1920  PRINT B$
1930  C7=0
1940  PRINT '10"WHAT IS THE ";
1950  W5=0
1960  PRINT "P(FIRST ";
1970  IF S2=1 THEN 1990
1980  GOTO 2010
1990  PRINT " TOSS ";
2000  GOTO 2030
2010  PRINT S2;
2020  GOSUB 4210
2030  PRINT " BEING ";
2040  GOSUB 4110
2050  PRINT " AND THE LAST "
2060  IF T1-S2=1 THEN 2080
2070  GOTO 2100
2080  PRINT " TOSS ";
2090  GOTO 2120
2100  PRINT T1-S2;
2110  GOSUB 4260
2120  PRINT " BEING ";
2130  GOSUB 4160
2140  IF W5=5 THEN 3360
2150  PRINT ")?";
2160  GOSUB 3670
2170  IF ABS(P-P8*Q8)<.001 THEN 2290
2180  C7=C7+1
2190  IF C7=1 THEN 2270
2200  GOSUB 4390
2210  IF C8=1 THEN 1940
2220  PRINT "THE ANSWER IS ";
2230  V5=(F1^S2)*(S1-F1)^(T1-S2)
2240  V6=(S1^S2)*S1^(T1-S2)
2250  GOSUB 4310
2260  GOTO 2330
2270  GOSUB 3900
2280  GOTO 1940
2290  PRINT B$
2300  GOTO 2330
2310  PRINT 
2320  PRINT '10"TRY AGAIN!"
2330  PRINT '10"IN HOW MANY WAYS CAN YOU GET EXACTLY"S2
2340  GOSUB 4110
2350  PRINT " AND "T1-S2;
2360  GOSUB 4160
2370  PRINT "?"
2380  INPUT Y2
2390  IF Y2=Y1 THEN 2930
2400  IF M4=5 AND N4=10 THEN 2490
2410  IF M4=5 THEN 2950
2420  PRINT 
2430  PRINT '10"HERE ARE A FEW WAYS IN WHICH YOU CAN GET EXACTLY"S2
2440  GOSUB 4110
2450  PRINT " AND "T1-S2;
2460  GOSUB 4160
2470  PRINT "."
2480  GOTO 2510
2490  PRINT "THE ANSWER IS "Y1
2500  GOTO 1140
2510  K=J=0
2520  PRINT 
2530  GOTO T1 OF 2660,2640,2620,2600,2580,2560,2540
2540  FOR A=1 TO 2
2550  N[7]=A
2560  FOR B=1 TO 2
2570  N[6]=B
2580  FOR C=1 TO 2
2590  N[5]=C
2600  FOR D=1 TO 2
2610  N[4]=D
2620  FOR E=1 TO 2
2630  N[3]=E
2640  FOR F=1 TO 2
2650  N[2]=F
2660  FOR G=1 TO 2
2670  N[1]=G
2680  J=J+1
2690  S=0
2700  FOR L=T1 TO 1 STEP -1
2710  A[J,L]=N[L]
2720  S=S+A[J,L]
2730  NEXT L
2740  IF S#2*S2+(T1-S2) THEN 2840
2750  FOR L=T1 TO 1 STEP -1
2760  IF A[J,L]=1 THEN 2790
2770  PRINT "S  ";
2780  GOTO 2800
2790  PRINT "F  ";
2800  NEXT L
2810  K=K+1
2820  IF K=INT(Y1/3)+1 THEN 2910
2830  PRINT 
2840  NEXT G
2850  NEXT F
2860  NEXT E
2870  NEXT D
2880  NEXT C
2890  NEXT B
2900  NEXT A
2910  M4=N4=5
2920  GOTO 2310
2930  M4=20
2940  PRINT C$
2950  PRINT "NOW, LOOK FOR A RELATIONSHIP BETWEEN THE NUMBERS IN"
2960  PRINT "PASCAL'S TRIANGLE AND THE NUMBER OF WAYS YOU"
2970  PRINT "CAN GET EXACTLY "S2;
2980  GOSUB 4110
2990  PRINT " AND "T1-S2;
3000  GOSUB 4160
3010  PRINT "."
3020  IF N4=10 THEN 3070
3030  Z1=10
3040  GOTO 30
3050  N4=10
3060  IF M4=5 THEN 3130
3070  PRINT "CAN YOU SEE THE RELATIONSHIP ";
3080  INPUT A$
3090  IF A$="YES" THEN 3200
3100  IF A$="NO" THEN 3130
3110  GOSUB 3880
3120  GOTO 3070
3130  PRINT "THE NUMBER OF THE ROW IS THE SAME AS THE NUMBER OF TIMES "
3140  PRINT "THAT THE POLYHEDRON WAS TOSSED.  THE NUMBERS IN EACH ROW"
3150  PRINT "ARE THE SAME AS THE NUMBER OF POSSIBLE WAYS OF GETTING SUCCESSES."
3160  PRINT "THE FIRST NUMBER IS THE NUMBER OF POSSIBLE WAYS OF GETTING"
3170  PRINT "0 SUCCESSES, THE SECOND NUMBER IS FOR 1 SUCCESS, ETC."
3180  IF M4=5 AND N4=10 THEN 2330
3190  GOTO 1140
3200  PRINT '10"CONGRATULATIONS!"
3210  GOTO 3230
3220  PRINT B$
3230  GOTO 1140
3240  PRINT C$
3250  PRINT "DO YOU WANT TO TRY ANOTHER PROBLEM";
3260  INPUT A$
3270  Z1=6
3280  U1=0
3290  IF A$=F$ THEN 560
3300  IF A$=E$ THEN 4510
3310  GOSUB 3880
3320  GOTO 3250
3330  PRINT "SUMMARIZING, YOU HAVE FOUND THE ";
3340  W5=5
3350  GOTO 1960
3360  V5=F1^S2*(S1-F1)^(T1-S2)
3370  V6=S1^S2*S1^(T1-S2)
3380  PRINT ")=";
3390  GOSUB 4310
3400  PRINT "THE NUMBER OF DIFFERENT WAYS THAT THIS EVENT COULD OCCUR IS"Y1
3410  M4=50
3420  GOTO 1140
3430  PRINT "SINCE EACH WAY HAS AN EQUAL PROBABILITY OF"
3440  PRINT V5"/"V6", AND SINCE THEY ARE MUTUALLY EXCLUSIVE, "
3450  PRINT "WE CAN ADD"V5"/"V6;Y1"TIMES = "Y1"*"V5"/"V6
3460  M4=100
3470  GOTO 1140
3480  REM- COMBINATIONS
3490  P1=P2=1
3500  X1=S2
3510  FOR K1=2 TO T1
3520  IF T1-X1 >= X1 THEN 3540
3530  GOTO 3570
3540  IF K1 <= X1 THEN 3600
3550  IF K1>T1-X1 THEN 3620
3560  GOTO 3630
3570  IF K1 <= T1-X1 THEN 3600
3580  IF K1>X1 THEN 3620
3590  GOTO 3630
3600  P1=P1*K1
3610  GOTO 3630
3620  P2=P2*K1
3630  NEXT K1
3640  Y1=P2/P1
3650  RETURN 
3660  REM-STUDENT INPUT FOR PROBABILITY
3670  PRINT TAB(5);
3680  ENTER 180,A1,N1
3690  IF N1=999 THEN 3770
3700  GOSUB 3810
3710  IF T2=1 THEN 3670
3720  PRINT TAB(8);"/";
3730  ENTER 180,A1,D1
3740  GOSUB 3810
3750  IF T2=1 THEN 3730
3760  GOTO 3780
3770  D1=1
3780  P=N1/D1
3790  PRINT 
3800  RETURN 
3810  T2=0
3820  IF A1#-256 THEN 3850
3830  PRINT "TAKE YOUR TIME."
3840  T2=1
3850  RETURN 
3860  PRINT '10"YOU HAVE INPUT AN INCORRECT NUMBER."
3870  RETURN 
3880  PRINT '10"YOU HAVE MADE A TYPING MISTAKE."
3890  RETURN 
3900  PRINT '10"ARE THESE EVENTS INDEPENDENT";
3910  INPUT A$
3920  IF A$=F$ THEN 3980
3930  IF A$=E$ THEN 3960
3940  GOSUB 3880
3950  GOTO 3900
3960  PRINT "REMEMBER THAT INDEPENDENT EVENTS DO NOT DEPEND ON EACH OTHER."
3970  GOTO 3990
3980  PRINT '10;B$
3990  PRINT '10"IF 2 EVENTS ARE INDEPENDENT THEN THE P(A&B)=P(A)?P(B)."
4000  PRINT "WHICH OF THE FOLLOWING OPERATORS BELONGS WHERE THE ? IS:"
4010  PRINT "1)ADD, 2)SUBTRACT, 3)MULTIPLY, OR 4)DIVIDE  (1,2,3, OR 4)  ";
4020  INPUT M1
4030  IF M1=3 THEN 4060
4040  PRINT "REFER TO THE DEFINITION AND TRY AGAIN."
4050  GOTO 3990
4060  PRINT C$
4070  PRINT "NOW, CALCULATE THE PROBABILITY AGAIN."
4080  PRINT "REMEMBER TO MULTIPLY THE PROBABILITIES."
4090  RETURN 
4100  END 
4110  IF S2=1 THEN 4140
4120  PRINT G$;
4130  GOTO 4150
4140  PRINT G$[1,7];
4150  RETURN 
4160  IF T1-S2=1 THEN 4190
4170  PRINT H$;
4180  GOTO 4200
4190  PRINT H$[1,7];
4200  RETURN 
4210  IF T1=1 THEN 4240
4220  PRINT J$;
4230  GOTO 4250
4240  PRINT J$[1,5];
4250  RETURN 
4260  IF T1-S2=1 THEN 4290
4270  PRINT J$;
4280  GOTO 4300
4290  PRINT J$[1,5];
4300  RETURN 
4310  FOR U=2 TO V5
4320  IF INT(V5/U)#V5/U OR INT(V6/U)#V6/U THEN 4360
4330  V5=V5/U
4340  V6=V6/U
4350  GOTO 4320
4360  NEXT U
4370  PRINT V5"/"V6"."
4380  RETURN 
4390  PRINT "NOW, WHICH DO YOU WANT TO DO:"
4400  PRINT "   1. TRY THE PROBLEM AGAIN,"
4410  PRINT "   2. HAVE THE CORRECT ANSWER PRINTED, OR"
4420  PRINT "   3. STOP RUNNING THE PROGRAM?"
4430  PRINT "INPUT 1,2, OR 3 ";
4440  INPUT C8
4450  PRINT 
4460  IF C8=3 THEN 4510
4470  IF C8=1 OR C8=2 THEN 4500
4480  GOSUB 3880
4490  GOTO 4390
4500  RETURN 
4510  PRINT "IS THERE A GENERAL FORMULA FOR CALCULATING THESE PROBABILITIES?"
4520  PRINT "IF P = P(SUCCESS), AND Q = P(FAILURE), THEN COMPLETE THE FOLLOWING:"
4530  PRINT 
4540  PRINT '10"P(X SUCCESSES)=P^";
4550  ENTER 180,A1,K$
4560  GOSUB 3810
4570  PRINT 
4580  PRINT 
4590  IF T2=1 THEN 4540
4600  IF K$="X" THEN 4640
4610  GOSUB 4390
4620  IF C8=1 THEN 4540
4630  PRINT '10"P(X SUCCESSES)=P^X"
4640  PRINT "P((N-X)FAILURES)=Q^(";TAB(23);")";
4650  PRINT '13TAB(20);
4660  ENTER 180,A1,K$
4670  GOSUB 3810
4680  PRINT 
4690  IF T2=1 THEN 4640
4700  IF K$="N-X" THEN 4740
4710  GOSUB 4390
4720  IF C8=1 THEN 4640
4730  PRINT '10"P((N-X)FAILURES)=Q^(N-X)"
4740  PRINT "COMPLETE THE FOLLOWING:"
4750  PRINT "IF EXACTLY X SUCCESSES AND N-X FAILURES CAN OCCUR R TIMES,"
4760  PRINT "THEN THE PROBABILITY THAT AN EXPERIMENT RESULTS IN EXACTLY X"
4770  PRINT "SUCCESSES AND N-X FAILURES = (LEAVE NO SPACES IN THE FORMULA)"
4780  PRINT "     P(X SUCCESS AND N-X FAILURES) = ";
4790  INPUT K$
4800  IF K$=L$[1,13] THEN 4900
4810  IF K$=L$[15,27] THEN 4900
4820  IF K$=L$[3,15] THEN 4900
4830  IF K$=L$[17,29] THEN 4900
4840  IF K$=L$[25,37] THEN 4900
4850  IF K$=L$[31,43] THEN 4900
4860  GOSUB 4390
4870  IF C8=1 THEN 4740
4880  PRINT "P(X SUCCESSES AND N-X FAILURES)="L$[1,13]
4890  GOTO 4920
4900  PRINT "THAT IS THE CORRECT FORMULA FOR CALCULATING THE PROBABILITY"
4910  PRINT "OF EACH INDIVIDUAL EVENT IN THE BINOMIAL PROBABILITY DISTRIBUTION."
4920  PRINT 
4930  PRINT "ANOTHER WAY TO CALCULATE THE PROBABILITIES IS THE FOLLOWING:"
4940  PRINT "R IS ACTUALLY A COMBINATION OF N THINGS TAKEN X AT A TIME WHERE"
4950  PRINT "N IS THE NUMBER OF TOSSES AND X IS THE EXACT NUMBER OF SUCCESSES."
4960  PRINT "IF C(N,X) = THE NUMBER OF COMBINATIONS OF N OBJECTS TAKEN "
4970  PRINT "X AT A TIME, THEN"
4980  PRINT "THE GENERAL FORMULA FOR CALCULATING THIS IS:"'10
4990  PRINT "C(N,X) = N!/(X!*(N-X)!)"
5000  PRINT "   (! STANDS FOR FACTORIAL -  5! = 1*2*3*4*5 = 120)"
5010  PRINT '10"YOU SHOULD CHECK A PROBABILITY BOOK FOR A MORE PRECISE"
5020  PRINT "EXPLANATION OF PERMUTATIONS AND COMBINATIONS."
5030  PRINT '10"----- DEFINITION:"
5040  PRINT '10"BINOMIAL PROBABILITY DISTRIBUTION- IF AN EXPERIMENT"
5050  PRINT "CONSISTS OF N INDEPENDENT BINOMIAL TRIALS, EACH WITH PROBABILITY"
5060  PRINT "P OF SUCCESS AND PROBABILITY Q (Q = 1-P) OF FAILURE, THEN"
5070  PRINT "THE PROBABILITY THAT THE EXPERIMENT RESULTS IN EXACTLY"
5080  PRINT "X SUCCESSES AND N-X FAILURES IS ="
5090  PRINT "    C(N,R) * P^X * Q^(N-X)"
5100  PRINT "       X = 0,1,2,3,...N"
5110  END 
