Exercise 4 - Probability

  1. A coin is tossed 4 times. Write a program, to calculate probability of getting
    • exactly four heads
    • at least two heads
    • no heads
    Compare your results with the analytic solutions.

  2. A pair of dice is tossed. Write a program to find the probability of getting 6:6.
    Compare your results with the analytic solutions.

  3. A fair dice is tossed 7 times. Write a program to find the probability of getting:
    • exactly four ONE
    • at least four ONE
    • no ONE
    Compare your results with the analytic solutions.

  4. A woman has N children, the probability of each child being female is 50%.
    Copy the program below and modify it to determine the probability of all the N children being female.
    Write a program to determine the probability for N = 1, 2, 3, .... 12.
    Compare your results with the analytic solutions. 
    
PROGRAM Births
!--------------------------------------------------------
! This program takes random numbers (generated uniformly
! between 0. and 1.)  and assigns  the sex of a child as
! either  male (M)  or  female (F)  according  to  a 50%
! probability for each case.
!--------------------------------------------------------
  IMPLICIT NONE
  INTEGER :: I
  CHARACTER(1) :: Sex
  REAL :: R
  DO I = 1, 6
    CALL RANDOM_NUMBER(R)
    IF (R < 0.5) THEN
      Sex = "M"
    ELSE
      Sex = "F"
    END IF
    PRINT *, Sex
  END DO
END PROGRAM Births