An unfair coin with Pr[H] = 2/3 is flipped. If the flip results in a head, then a marble is selected from an urn containing 9 red, 1 white, and 1 blue marbles. If the flip results in a tail then a marble is selected from an urn containing 10 red and 3 white marbles. If the marble selected is white, then what is the probability that a flip resulted in a head?