Question

saada buys a bag of cookies that contains 4 chocolate chip cookies, 7 peanut butter cookies, 6 sugar cookies and 9 oatmeal cookies. what is the probability that saada randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie? express you answer as a reduced fraction.

Explanation:

Step1: Calculate total cookies initially

Total cookies = 4 + 7 + 6 + 9 = 26.

Step2: Probability of first selecting sugar cookie

Number of sugar cookies = 6. Probability \( P(\text{sugar}) = \frac{6}{26} = \frac{3}{13} \).

Step3: Calculate total cookies after eating sugar cookie

New total = 26 - 1 = 25.

Step4: Probability of selecting oatmeal cookie next

Number of oatmeal cookies = 9. Probability \( P(\text{oatmeal after sugar}) = \frac{9}{25} \).

Step5: Multiply the two probabilities (since events are sequential)

\( P = \frac{3}{13} \times \frac{9}{25} = \frac{27}{325} \). Wait, no—wait, the problem is: first select sugar, eat it, then select oatmeal. Wait, no, the problem is: "randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie". So it's the probability of first sugar, then oatmeal. Wait, but let's recheck total initial: 4 +7 +6 +9 = 26. So first, probability of sugar: 6/26. Then, after removing one sugar, total is 25, oatmeal is 9. So probability is (6/26)(9/25). Simplify 6/26 to 3/13. Then 3/13 9/25 = 27/325. Wait, but let's check again. Wait, maybe I misread: the bag has 4 chocolate, 7 peanut butter, 6 sugar, 9 oatmeal. So total 4+7=11, 11+6=17, 17+9=26. Correct. So first event: pick sugar (6 out of 26), then pick oatmeal (9 out of 25, since one cookie is removed). So multiply the two probabilities. So (6/26)(9/25) = (3/13)(9/25) = 27/325. Is 27 and 325 coprime? 325 is 5513. 27 is 333. No common factors. So 27/325. Wait, but maybe I made a mistake. Wait, the problem says "randomly selects a sugar cookie from the bag, eats it, then randomly selects an oatmeal cookie". So it's the probability of first sugar, then oatmeal. So yes, that's the calculation.

Answer:

\(\frac{27}{325}\)