f90: Define the type of sampling. Give the set and sample sizes and find the number of possibilities and the probability for each possibility *.exe and *.out are the Windows and Linux executables.

smpl_prob.exe

smpl_prob.f90

PROGRAM smpl_prob

! Declarations
INTEGER:: i, k, m, n, o, p, s, po
INTEGER::a, b, c=1, d, e, f=1, g, h, l=1
REAL:: pr
CHARACTER(1):: exiit

! Opening prints

PRINT*,
PRINT*,
PRINT*, 'This program is written by Mohammad A. Nilforooshan.'
PRINT*, 'All rights reserved.'
PRINT*, 'http://sites.google.com/site/mannprofile/'

! Ask the type of sampling

PRINT*,
PRINT*,
PRINT*, 'Please define the type of sampling.'
PRINT*,
PRINT*, 'Examples:'
PRINT*, 'Coin-tossing is a sampling with replacement.'
PRINT*, 'In an order independent sampling "AB" and "BA" are the same.'
PRINT*,
PRINT*, '- with    replacement and order   dependent (press 1)'
PRINT*, '- with    replacement and order independent (press 2)'
PRINT*, '- without replacement and order   dependent (press 3)'
PRINT*, '- without replacement and order independent (press 4)'
PRINT*, 'Press any other key to exit.'
READ*, s

IF ((s/=1) .AND. (s/=2) .AND. (s/=3) .AND. (s/=4)) STOP

! Ask the input values

PRINT*,
PRINT*,
PRINT*, 'Set size?'
PRINT*, 'e.g., in coin-tossing, no matter how many times'
PRINT*, 'you repeat it, the set size is equal to 2.'
READ*, n

45 PRINT*,
PRINT*,
PRINT*, 'Sample size?'
PRINT*, 'e.g., in coin-tossing, it is the number of times you toss the coin.'
READ*, m
PRINT*,
PRINT*,

o=n-m

IF ((s>2) .AND. (o<0)) THEN
    PRINT*, 'In a sampling without replacement,'
    PRINT*, 'the set size should be greater than the sample size.'
    GO TO 45
END IF

! Estimate the factorials

a=n
d=o
g=m

IF (s>2) THEN
    DO i=1,n/2
        b=a*(a-1)
        c=c*b
        a=a-2
    END DO
    DO i=1,o/2
        e=d*(d-1)
        f=f*e
        d=d-2
    END DO
END IF
! n!=c
! (n-m)!=f


IF (s==4) THEN
    DO i=1,m/2
        h=g*(g-1)
        l=l*h
        g=g-2
    END DO
END IF
! m!=l

! Calculate the number of possibilities and probilities

IF (s==1) THEN
    po=n**m
END IF

IF (s==2) THEN
    k=n
    p=0
    po=0
    DO i=1,n
        p=i*(k**(m-2))
        po=po+p
        k=k-1
    END DO
    WRITE(*,*) 'Possibilities=',po
    PRINT*, 'Probabilities are different for different possibilities.'
    STOP
END IF

IF (s==3) THEN
    po=c/f
END IF

IF (s==4) THEN
    po=c/(f*l)
END IF

pr=1/REAL(po)

! Print the results on the screen

WRITE(*,*) 'Possibilities=',po
WRITE(*,*) 'Probability  =',pr

! Finished

PRINT*,
PRINT*,
PRINT*, 'Press any key to exit.'
READ*, exiit

IF (exiit=='a') THEN
GO TO 138
END IF

138 END PROGRAM smpl_prob

smpl_prob.out