Cristina buys a bag of cookies that contains 8 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.

What is the probability that Cristina reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie?

 

The probability that Cristina reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie is 0.0788177.

(Round your final answer to the required decimals.)

Step-by-step explanation

Cristina buys a bag of cookies that contains 8 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.

So, before eating, the total number cookies is:

• Total cookies = 8 chocolate chip +8 peanut butter + 5 sugar + 8 oatmeal = 29 cookies.

At first, the probability that Cristina reaches in the bag and randomly selects a peanut butter cookie from the bag;

• P(Peanut) = total peanut cookies/total number of cookies
• P(Peanut) = 8/29

At second eating, the remaining cookies are 28 cookies, so the probability that Cristina reaches in the bag and randomly selects an oatmeal cookie from the bag;

• P(oatmeal) = total oatmeal cookies/total number of remaining cookies
• P(Oatmeal) = 8/28

Thus, the probability that Cristina reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie;

• P(Peanut then Oatmeal) = (8/29)*(8/28)
• P(Peanut then Oatmeal) = 16/203 0r 0.0788177