Question

Holly buys a bag of cookies that contains 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookiesand 8 oatmeal cookies.What is the probability that Holly reaches in the bag and randomly selects an oatmeal cookie from the bag,eats it, then reaches back in the bag and randomly selects a peanut butter cookie?Give your answer as a fraction, or accurate to at least 4 decimal places.

Answer 1

The bag contains: 4 chocolate chip cookies, 4 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies.

Therefore, there is a total of 24 cookies.

Thus, the probability of selecting an oatmeal cookie (8) from the bag (24) is: 1/3

`P_1=(8)/(24)=(1)/(3)\approx0.3333\ldots`

After she eats this cookie, there are 23 cookies left.

Now, the probability of selecting a peanut butter cookie (4) from the bag (23) is: 4/23

`P_2=(4)/(23)=0.17391\approx0.1739`

Now, the probability of these two events to happen, is the following: 4/69

`\begin{gathered} P_(1\&2)=P_1\cdot P_2=(8)/(24)\cdot(4)/(23) \\ =(1)/(3)\cdot(4)/(23) \\ =(4)/(69) \\ \approx0.0580 \end{gathered}`