Question

heather buys a bag of cookies that contains 4 chocolate chip cookies, 8 peanut butter cookies, 6 sugar cookies and 8 oatmeal cookies. what is the probability that heather 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? write your answer as a percent. round to the nearest tenth of a percent. answer: %

Explanation:

Step1: Calculate total number of cookies

$4 + 8+6 + 8=26$

Step2: Calculate probability of first - selecting an oatmeal cookie

The number of oatmeal cookies is 8. The probability $P_1$ of selecting an oatmeal cookie first is $\frac{8}{26}$.

Step3: Calculate probability of second - selecting a peanut butter cookie

After eating an oatmeal cookie, there are 25 cookies left. The number of peanut butter cookies is 8. The probability $P_2$ of selecting a peanut butter cookie second is $\frac{8}{25}$.

Step4: Calculate the combined probability

Since these are independent - dependent events, the combined probability $P = P_1\times P_2=\frac{8}{26}\times\frac{8}{25}=\frac{64}{650}\approx0.09846$.

Step5: Convert to percentage and round

$0.09846\times100 = 9.846\%$. Rounding to the nearest tenth of a percent gives $9.8\%$.

Answer:

$9.8\%$