Bayes theorem on Conditional probability problem solution

Question

Problem Statement: Consider 3 bags. Bag A contains 2 white balls and 4 red balls; Bag B contains 8 white balls and 4 red balls, Bag C contains 1 white ball and 3 red balls. We draw 1 ball from each bag. What is the probability to draw a white ball from Bag A if we know that we drew exactly a total of 2 white balls total? Solution