Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine boys in ten births.

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Quizplus · Accepted Answer

The probability of exactly nine boys in ten births can be calculated using the binomial probability formula, which is $P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$, where $n$ is the number of trials (in this case, 10 births), $k$ is the number of successful outcomes desired (in this case, 9 boys), and $p$ is the probability of success on any given trial (in this case, 0.5, since each birth is equally likely to be a boy or a girl). Plugging in the values, we get $P(X=9) = \binom{10}{9}(0.5)^9(0.5)^{10-9} = 10(0.5)^{10} = 0.010$.

Assume That Male and Female Births Are Equally Likely and That