Question

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?

Answer 1

0.1248 = 12.48% probability of getting 3 blues.

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:

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

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:

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

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

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

Sample of 5 means that
`n = 5`

7 blue means that
`k = 7`

What is the probability of getting 3 blues?

This is P(X = 3).

`P(X = x) = h(x,N,n,k) = (C_(k,x)*C_(N-k,n-x))/(C_(N,n))`

`P(X = 3) = h(3,23,5,7) = (C_(7,3)*C_(16,2))/(C_(23,5)) = 0.1248`

0.1248 = 12.48% probability of getting 3 blues.