Simon Has Two Urns, 1 and 2

Multiple Choice

Simon has two urns, 1 and 2. Urn 1 contains two white and 1 black pawn. Urn 2 contains 1 white and 2 black pawns. Simon tosses a regular 6-sided die. If the die comes up with 1 through 4, Simon chooses Urn 1, while if the die comes up with 5 or 6, he chooses Urn 2. Once an urn is chosen, he reaches in and randomly picks out a pawn from that urn. Suppose Simon picks a black pawn. What is the probability that the black pawn came from Urn 1?

A) 1/9.
B) 1/2.
C) 1/3.
D) 2/3.