Final answer:
The probability that Betty randomly selects an oatmeal cookie and then a sugar cookie from the bag is 20/253.
Step-by-step explanation:
The question involves calculating the probability of two dependent events: 1) Betty selecting an oatmeal cookie, and 2) then selecting a sugar cookie. Since there are 4 chocolate chip cookies, 6 peanut butter cookies, 8 sugar cookies, and 5 oatmeal cookies, the total number of cookies is 23. The probability of first selecting an oatmeal cookie is the number of oatmeal cookies over the total, which is 5/23. After eating an oatmeal cookie, there are now 22 cookies left. The probability of then selecting a sugar cookie is the number of sugar cookies over the new total, which is 8/22 or 4/11 after reduction. To find the combined probability of both events occurring, we multiply the probabilities of each event: (5/23) × (4/11), which simplifies to 20/253. Therefore, the reduced fraction representing the probability that Betty randomly selects an oatmeal cookie and then a sugar cookie is 20/253.