I believe this problem has 3 questions:
a. Explain why the three conditions are satisfied for X to have the binomial distribution.
b. Identify n and p for the binomial distribution.
c. Find the probability that the family has two girls and two boys.
Answers:
a. First because there are only 2 possible outcomes for
each birth: male or female. Hence a binomial distribution.
Second, because the probability of giving out a girl is
constant: 0.49 for each birth.
Third, the probability of a giving out a girl does not depend
on whether or not there is already a boy or a girl in the family.
b. The n is the total number of children, so n = 4
While the p is the success of being a girls, so P = 0.49
c. We use the binomial probability equation:
P (X) = nCx * p^x * q^(n-x)
P(X=2) = 4!/(2!2!) * 0.49^2 * 0.51^2 = 0.3747
