How do I apply the binomial distribution formula

Question

How do I apply the binomial distribution formula for the following problem?

Assume that 15% of the population is allergic to cats. If you randomly select 60 people for a medical trial, what is the probability that 7 of those people are allergic to cats?

Answer 1

Here you have the binomial distribution with $n=60$ trials (the $60$ people) and with a probability of success $p=15\%=0.15$; the random variable here is $X=\text{number of people with the allergy}$. So apply the binomial distribution formula to find the probability $\mathbf{P}\{X=7\}$.

Answer 2

Well, you have a Bernoulli trail with $n=60$, $p=0.15$ and $k=7$. The probability is

$P(X=k) = {n\choose k} p^k(1-p)^{n-k}.$