# Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar

Discussion in 'Calculator Requests' started by math_celebrity, May 20, 2020.

1. ### math_celebrityAdministratorStaff Member

Aaron buys a bag of cookies that contains 8 chocolate chip cookies, 6 peanut butter cookies,7 sugar cookies and 6 oatmeal raisin cookies. What it’s the probability that Aaron randomly selects a peanut butter cookie from the bag, eats it,, then randomly selects another peanut butter cookie?

First draw out of the bag is a peanut butter cookie:
P(PB) = Total Peanut Butter Cookies / Total Cookies
P(PB) = 6/27

Second draw out of the bag is a peanut butter cookie, but we have one less since Aaron ate one:
P(PB) = Total Peanut Butter Cookies - 1 / Total Cookies - 1
P(PB) = (6 - 1)/(27 - 1)
P(PB) = 5/26

Now, since each event is independent, we multiply them to see the probability of choosing a peanut butter cookie, eating it, then reaching in and choosing another peanut butter cookie:
P(PB, PB) = 6/27 * 5/26
P(PB, PB) = 5/117