Marnie is counting migratory birds that return annually to Smallville, a small residential area. The first year she tags 400 birds. The second year she counts 450 tagged birds over the course of three months.

There are three bags: a (contains 2 white and 4 red balls), b (8 white, 4 red) and c (1 white 3 red). you select one ball at random from each bag, observe that exactly two are white, but forget which ball came from which bag. what is the probability that you selected a white ball from bag a?