Final answer:
To find the probability that the candy Oscar selected on Tuesday was also a bon bon, we can use conditional probability. We calculate the conditional probability by dividing the probability of both candies being bon bons by the probability of selecting a bon bon on Wednesday. The probability is found to be 13/20.
Step-by-step explanation:
To find the probability that the candy Oscar selected on Tuesday was also a bon bon, we can use conditional probability. Let A be the event that the selected candy on Wednesday is a bon bon, and let B be the event that the selected candy on Tuesday is also a bon bon. We want to find P(B|A), the probability of B given A.
Using the formula for conditional probability, P(B|A) = P(B ∩ A) / P(A).
P(B ∩ A), the probability that both candies are bon bons, can be calculated as the product of the probabilities of selecting a bon bon from each bag: (6/13) * (9/14) = 54/182 = 27/91.
P(A), the probability of selecting a bon bon on Wednesday, can be calculated by considering both cases: selecting a bon bon from the first bag and transferring it to the second bag, and selecting a bon bon directly from the second bag. The probability of the first case is (6/13) * (3/15) = 18/195, and the probability of the second case is (9/14) * (4/15) = 36/210. So, P(A) = (18/195) + (36/210) = 12/65.
Now we can calculate P(B|A) = (27/91) / (12/65) = (27/91) * (65/12) = 13/20.
Therefore, the probability that the candy Oscar selected on Tuesday was also a bon bon, given that the candy he selected on Wednesday was a bon bon, is 13/20. Answer choice B, 41/20, is incorrect.