In a family of 6 children, what is the probability

Bevan Mcdonald 2021-10-02 Answered
In a family of 6 children, what is the probability of getting exactly 5 boys?

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Expert Answer

au4gsf
Answered 2021-10-03 Author has 9833 answers
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
Answer:
The probability of getting Exactly 5 boys is 0.09375.
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