Question

The Wilson family was one of the first to come to the U.S. They had 9 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had:

at least 2 girls?

at most 3 girls?

Answer 1

Prob(at least 2 girls)
= 1 - prob(no girls) - prob(exactly 1 girl)
= 1 - C(9,0) (1/2)^0 (1/2)^9 - C(9,1) (1/2) (1/2)^8
= 1 - (1/2)^9 - 9(1/2)^9
= 1 - 1/512 - 9/512
= 251/512 or appr .98

prob(at most 3 girls)
prob(exactly 1 girl) + prob(exactly 2 girls) + prob(exactly 3 girls)
= .....