Box 1 contains 5 red and 3 blue marbles while box 2 contains 2 red, 3 blue, and 1 white marble
If you select box 2 and select a marble at random from it, then toss that marble into the other box and randomly draw a marble from it, what is the probability that the marble you draw is blue?
Suggest you approach it this way: Half the time the marble pulled from box 2 is blue, and half the time it's not. So half the time box 1 ends up with 4 out of 9 marbles that are blue, and half the time it ends up with just 3 out of 9 that are blue. So the probability of pulling a blue from box 1 is the average of 3/9 and 4/9.