Question

The Jones family was one of the first to come to the U.S. They had 6 children. Assuming that the probability of a child being a girl is .5, find the probability that the Jones family had: at least 3 girls? at most 5 girls?

Answer 1

This is a case of binomial distribution with n = 6 and p = 0.5

we will use the following formula

P(X=r) =

(A) P(at least 3) = 1 - P(x at most 2)

= 1- P(X=0) - P(X=1) - P(X=2)

where

So, we get

P(X at least 3) = 1 - 0.0156 - 0.0938 - 0.2344

= 1-0.3437

= 0.6533

(B) P(at most 5 girls) =1 - P(X=6)

where

So, we get

P(at most 5 girls) = 1-0.0156

= 0.9844