(solution) Box A contains three red balls and two white balls; box B contains two red balls and two white…

(solution) Box A contains three red balls and two white balls; box B contains two red balls and two white…

Box A contains three red balls and two white balls; box B contains two red balls and two white balls. A fair die is thrown. If the upper face of the die shows 1 or 2, a ball is drawn at random from box A and put in box B and then a ball is drawn at random from box B. If the upper face of the die shows 3, 4, 5 or 6, a ball is drawn at random from box B and put in box A, and then a ball is drawn at random from box A. What are the probabilities (a) That the second ball drawn is white? (b) That both balls drawn are red? (c) That the upper face of the red die showed 3, given that one ball drawn is white and the other red?