Question

A cat has a litter of 7 kittens. find the probability that exactly 5 of the little furballs (kittens) are female. assume that male and female births are equally likely. use the binomial probability formula or the binomial probability table. if you use the binomial probability table, chhose the nearest answer.

Answer 1

The probability 0.1641.

The binomial distribution is

$_nC_r(p)^r(1-p)^{n-r}$

For this problem, we have:
$_7C_5(0.5)^5(1-0.5)^{7-5} \\ \\=\frac{7!}{5!2!}(0.5^5)(0.5)^2=0.1641$