# What is the probability of getting 6 girls in 8 births?

#### Answer:

$\left(\begin{matrix}8 \\ 6\end{matrix}\right) {\left(\frac{1}{2}\right)}^{6} {\left(\frac{1}{2}\right)}^{2} = \frac{28}{256} = 0.109375$

#### Explanation:

The probability of getting a girl is $\frac{1}{2}$. The probability of getting 6 girls is therefore ${\left(\frac{1}{2}\right)}^{6}$.

Since we have 6 girls, we also need to find the probability of getting 2 boys, which is ${\left(\frac{1}{2}\right)}^{2}$.

There are $\left(\begin{matrix}8 \\ 6\end{matrix}\right) = 28$ ways to get 6 girls out of 8 children.

This all gives:

$28 {\left(\frac{1}{2}\right)}^{6} {\left(\frac{1}{2}\right)}^{2} = \frac{28}{256} = 0.109375$