Question

A survey found that 25% of pet owners had their pets bathed proffesionally rather than doing it themselves. If 18 pet owners are randomly selected, the probability that exactly 5 people have their pets bathed proffesionally is
A. 19.99%
B. 19.88%
C. 18.99%
D. 18.88%

Answer 1

The probability is 19.88%.

This is a binomial distribution, because there are two outcomes, the events are independent of each other, and there is a fixed number of trials.  The binomial distribution is given by:

$(_k^n)p^k(1-p)^{n-k}$

For this, n is 18; k is 5; p is 0.25:
$(_5^{18})(0.25)^5(1-0.25)^{18-5} \\ \\=\frac{18!}{5!13!}(0.25)^5(0.75)^{13} \\ \\=8568(0.25)^5(0.75)^{13} \\=0.1988=19.88%$