'HW 3
'PROBLEM 2
'BY SONAL NAIK
************************************************************
DECLARE SUB PROBLEM ()
DECLARE FUNCTION EXACT (N1, P)
DECLARE FUNCTION SIMULATED (P, K, N1)

'FUNCTIONS WILL RETURN THE PROBABILITY OF GETTING FIRST SUCCESS IN K-th PICK

CLS
PROBLEM
PRINT ""
RANDOMIZE TIMER
PRINT "ENTER THE NUMBER OF THE FIRST SUCCESS"
INPUT K
PRINT ""
PRINT "ENTER THE PROBABILITY OF A SUCCESS"
INPUT P
PRINT ""
PRINT "THE EXACT PROBABILITY:                  "; EXACT(K, P)
PRINT "SIMULATED PROBABILITY:  1000 SIMULATIONS"; SIMULATED(P, K, 1000)
PRINT "SIMULATED PROBABILITY:  5000 SIMULATIONS"; SIMULATED(P, K, 5000)
PRINT "SIMULATED PROBABILITY: 10000 SIMULATIONS"; SIMULATED(P, K, 10000)
END

FUNCTION EXACT (K, P)
EXACT = P * (1 - P) ^ (K - 1)
END FUNCTION

SUB PROBLEM
'introduce the problem
PRINT "WHAT IS THE PROBABILITY OF THE FIRST SUCCESS OCCURING"
PRINT "IN THE KTH TRIAL IF THE PROBABILITY OF SUCCESS IS P"
PRINT "CHECK HOW THE SIMULATED PROBABILITY GETS CLOSER TO "
PRINT "THE EXACT PROBABILITY AS THE NUMBER OF SIMULATIONS INCREASES"
END SUB

FUNCTION SIMULATED (P, K, N1)
CTR = 0
FOR I = 1 TO N1
 '**********************Function: Sim1Geom(p) **************
 '* Usage; L=Sim1Geom(p)
 FOR L = 1 TO K
    IF RND(1) < P THEN IF L <> K THEN EXIT FOR ELSE CTR = CTR + 1
 NEXT L
 '********************** end of Function Sim1Geom(p) *******
NEXT I
SIMULATED = CTR / N1
END FUNCTION