Question

Given that 51.3% of all newly born children are boys, then what is the probability that in a sample of 5 newly born children, exactly 3 are boys?

Answer 1

Answer for Question #71979

Probability of a boy's birth

$$p = 51.3\% = 0.513 \quad \Rightarrow \quad q = 1 - p = 0.487$$

Under the Bernoulli formula, the probability that among the 5 newborns will be exactly 3 boys is

$$P_{5}(3) = \binom{5}{3} p^{3} q^{2} = \frac{5!}{3! \cdot 2!} \cdot 0.513^{3} \cdot 0.487^{2} = 0.3202 = 32.02\%$$

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