Question

1. a jar contains 6 chocolate, 9 peanut butter, and 11 oatmeal cookies. you reach into the jar, pick a cookie, and then eat it. delighted, you pick another cookie to snack on later. what is the probability of randomly choosing a peanut butter cookie first, then choosing a second one that is not oatmeal?

Explanation:

Step1: Calculate total cookies initially

Total cookies = 6 + 9 + 11 = 26.

Step2: Probability of peanut butter first

Probability (peanut butter first) = $\frac{9}{26}$.

Step3: Calculate remaining cookies and non - oatmeal cookies after first pick

After eating one peanut butter cookie, remaining cookies = 26 - 1 = 25.
Non - oatmeal cookies remaining = (6 + 9 - 1) = 14 (since we ate one peanut butter, original chocolate (6) + remaining peanut butter (9 - 1 = 8) = 14).

Step4: Probability of non - oatmeal second

Probability (non - oatmeal second) = $\frac{14}{25}$.

Step5: Multiply the two probabilities

Final probability = $\frac{9}{26}×\frac{14}{25}=\frac{126}{650}=\frac{63}{325}$.

Answer:

$\frac{63}{325}$