A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial. The director is going to choose 8 of these kittens at random to be in the commercial.
What is the probability that the director chooses 3 boy kittens and 5 girl kittens? Round your answer to three decimal places.

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

Step-by-step explanation:

The kittens are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.

This means that

We want 3 boys, so

The director is going to choose 8 of these kittens at random to be in the commercial.

This means that

What is the probability that the director chooses 3 boy kittens and 5 girl kittens?

This is P(X = 3).

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.