Question

The Smith family was one of the first to come to the U.S. They had 8 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had:

a. at least 6 girls
b. at most 5 girls

Answer 1

Use binomial distribution because:
1. Bernoulli trials (either girl or boy)
2. number of trials (n=9) known.
3. probability (p=0.5) of outcome known and remains constant throughout trials
4. trials are independent of each other.

n=9
p=0.5
P(X=k)=C(n,k)*p^k*(1-p)^(n-k)
where
C(n,k) is the number of combinations of k objects taken from n.

At least 5 girls means X=5,6,7,8,9
So
P(X>=5)
=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)
=0.24609+0.16406+0.07031+0.01758+0.00195
=0.5000