The Smith Family

Question

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

at least 3 girls?

at most 4 girls?

Answer 1

(5 choose 3) (1/2)^3 (1/2)^2 + (5 choose 4) (1/2)^4 (1/2) + (5 choose 5) (1/2)^5 (1/2)^0 =

10 /32 + 5/32 + 1/32 = 16/32 = 1/2

at most 4 = 0,1,2,3,4

Prob(at most 4) = 1 - Prob( 5) = 1 - (5 chooe 5)(1/2)^5(1/2)^0 = 1 - 1/32 = 31/32