Question

In a given population, the percent of people with blue eyes is 32%. If 17 people from that population are randomly selected, what is the probability that exactly 9 of them will have blue eyes?

Answer 1

The required probability is 0.0391.

Explanation:

Consider the provided information.

The percent of people with blue eyes is 32%

Thus, p = 32% = 0.32

The percent of people with non blue eyes is 100%-32%=68% = 0.68

q = 68% = 0.68

We need to determine the probability that exactly 9 of them will have blue eyes if 17 are selected.

Thus, n=17 and r=9

Use the formula of binomial distribution:
`P(r) = ^nC_r p^r q^(n-r)`

Substitute the respective values in the above formula.

`P(r=9) = ^(17)C_9 *(0.32)^9 * 0.68^(17-9)`

`P(r=9) = (17!)/(9!8!) *(0.32)^9 * 0.68^(8)`

`P(r=9) \approx0.0391`

Hence, the required probability is 0.0391.