Question

The Smith 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 Smith family had: at least 7 girls ? at most 8 girls?

Answer 1

We will have the following:

***Having at least 7 girls:

`\begin{gathered} P(x\ge7)=(9!)/(7!(9-7)!)(0.5)^7(0.5)^(9-7)+(9!)/(8!(9-8!))(0.5)^8(0.5)^(9-8) \\ \\ \Rightarrow P(x\ge7)=(45)/(512)\Rightarrow P(x\ge7)\approx0.088 \end{gathered}`

The probability is 45/512, that is approximately 0.088.

***Having at most 8 girls:

So, the probability of having at most 8 girls is 511/512, that is approximately 0.99.