Suppose that each child born to a couple is equally likely t

Suppose that each child born to a couple is equally likely to be a boy or a girl independent of the sex distribution of the other children in the family. For a couple having 5 children, compute the probabilities of the following events: a. All children are of the same sex. b. The 3 eldest are boys and the other girls. c. Exactly 3 are boys. d. The 2 oldest are girls. e. There is at least 1 girl

Solution

using binomial distribution

a)

Probability = 5C5 * (1/2)^5 * (1/2)^5-5 = 0.03125

b)

geometric distrbituion

P= 1/2^(3-1) * 1/2 = 0.125

c)

binomial distribution

P(x=3) = 5C3 * 1/2^3 * 1/2^(5-3) = 0.3125

d)

geomtric distribution

P = (1/2)^(2-1) * 1/2 = 0.25

e)

P ( x >= 1 ) = 1 - P( x < 1 ) = 1 - P(x=0)

P(x=0 ) = 5C0 * 1/2^0 * 1/2^5-0 = 0.03125

P( x >= 1 ) = 1 - 0.03125 = 0.96875