WHAT IS THE PROBABILITY THAT BOTH BALLS COME FROM URN B?

Question

URN A CONTAINS TWO WHITE , 1 BLACK AND THREE RED BALLS  URN B CONTAINS 3 WHITE , 2 BLACK AND 4 RED BALLS AND URN C CONTAINS 4 WHITE , 3 BLACK AND 2 RED BALLS, ONE URN IS CHOSEN AT RANDOM AND 2 BALLS ARE DRAWN.THEY HAPPEN TO BE RED AND BLACK.WHAT IS THE PROBABILITY THAT BOTH BALLS CAME FROM URN B?

Answer 1

Urn A:  2 white, 1 black, 3 red.

Urn B:  3 white, 2 black, 4 red.

Urn C:  4 white, 3 black, 2 red.

One urn is chosen randomly, 2 balls drawn, a red and a black.

Probability of choosing urn B:  1/3

Within urn B, probability of choosing red or black on ball 1:  (2+4)/9 = 1/3

Within urn B, having chosen 1 red or black already, probability of choosing another red or black:  5/8

Probability urn B, then a red or black, then another red or black:  1/3 * 1/3 * 5/8 = 5/72 = 0.069444444 (4s forever).