Question

Heather buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 9 sugar cookies and 4 oatmeal cookies. What is the probability that Heather reaches in the bag and randomly selects 2 peanut butter cookies from the bag? Round your answer to four decimal places.

Answer 1

Answer:

0.0862 = 8.62% probability that Heather reaches in the bag and randomly selects 2 peanut butter cookies from the bag

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcoes.

The order in which the cookies are selected is not important, so we use the combinations formula to solve this question.

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.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

2 peanut butter cookies, from a set of 4. So

$D = C_{8,2} = \frac{8!}{2!6!} = 28$

Total outcomes:

2 cookies from a set of 5+8+9+4 = 26. So

$T = C_{26,2} = \frac{26!}{2!24!} = 325$

Probability:

$p = \frac{D}{T} = \frac{28}{325} = 0.0862$

0.0862 = 8.62% probability that Heather reaches in the bag and randomly selects 2 peanut butter cookies from the bag