Marble Transfer: Conditional Probability

You have two bins. Bin 1 contains $r_1 = 4$ red and $b_1 = 3$ blue marbles. Bin 2 contains $r_2 = 5$ red and $b_2 = 3$ blue marbles. You draw one marble uniformly at random from Bin 1 and drop it into Bin 2. Then you draw one marble uniformly at random from the now-enlarged Bin 2. What is the probability that the marble you draw from Bin 2 is blue?