# In a family of 6 children, what is the probability

In a family of 6 children, what is the probability of getting exactly 5 boys?

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Step 1
Given: $$\displaystyle{n}={6}$$
probability of boy $$\displaystyle{p}={0.5}$$
probability of girl $$\displaystyle{q}={0.5}$$
The probability of getting exactly 5 boys is obtained using Binomial probability as below:
$$\displaystyle{P}{\left({X}={5}\right)}=_{{{6}}}{C}_{{{5}}}{\left({0.5}^{{{5}}}\right)}{\left({0.5}^{{{6}-{5}}}\right)}$$
$$\displaystyle={6}\times{0.03125}\times{0.5}$$
$$\displaystyle={0.09375}$$
Thus, the probability of getting Exactly 5 boys is 0.09375.
Step 2
The probability of getting Exactly 5 boys is 0.09375.