Question

alexis buys a bag of cookies that contains 8 chocolate chip cookies, 9 peanut butter cookies, 8 sugar cookies and 9 oatmeal raisin cookies. what is the probability that alexis randomly selects an oatmeal raisin cookie from the bag, eats it, then randomly selects another oatmeal raisin cookie? express your answer as a reduced fraction.

Explanation:

Step1: Calculate total cookies initially

Total cookies = 8 (chocolate chip) + 9 (peanut butter) + 8 (sugar) + 9 (oatmeal raisin) = 34.
Probability first oatmeal raisin: $\frac{9}{34}$.

Step2: Calculate total cookies after first selection

After eating one oatmeal raisin, total cookies = 34 - 1 = 33.
Oatmeal raisin cookies left = 9 - 1 = 8.

Step3: Calculate probability of second oatmeal raisin

Probability second oatmeal raisin: $\frac{8}{33}$.

Step4: Multiply the two probabilities

Combined probability = $\frac{9}{34} \times \frac{8}{33}$ = $\frac{72}{1122}$ = $\frac{12}{187}$.

Answer:

$\frac{12}{187}$