A bag of M&Ms contains 7 blue, 4 brown, 4 orange, 2 yellow, 3 red, and 3 green. Reaching into the bag, a person grabs 5 M&Ms.
What is the probability of getting 3 blues?

0.1248 = 12.48% probability of getting 3 blues.

Step-by-step explanation:

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

Hypergeometric distribution:

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

In which:

x is the number of successes.

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.

In this question:

7 + 4 + 4 + 2 + 3 + 3 = 23 total M&Ms, which means that

Sample of 5 means that

7 blue means that

What is the probability of getting 3 blues?

This is P(X = 3).

0.1248 = 12.48% probability of getting 3 blues.