Suppose box A contains 2 red balls and 4 blue balls and box B contains 6 red balls and 3 blue ball. An experiment consists of drawing a ball from box A and then putting it in box B. A ball is then drawn from box B.

What is the probability the first ball drawn was red given the second ball drawn was red?

First of all, we do not know if the box is open or closed. If the box is open and the person drawing the ball can see them, the answer is 50/50 since there are only two colors to choose from. If the box was closed and the person drawing the ball could not see the colors of the balls, the odds of drawing a red ball would mathematically be 1 in 3 because there were 6 balls in all with 2 of them red (6:2 = 3:1). The second ball drawn - - the one from box B - - has no bearing on these odds. As usual, I could be wrong about this and would appreciate knowing the correct answer or, if I am in fact correct, I would also like to know that.