Help with Conditional Probability question (Urns and Balls)

Question

Urn A contains 3 red and 7 blue balls. Urn B contains 4 red and 5 white balls, and

Urn C contains 3 white and 6 blue balls. A ball is chosen at random from Urn A and

placed in Urn B. Then a ball is chosen at random from Urn B and placed in Urn C.

Finally, two balls are randomly chosen without replacement from Urn C.

Question: Find the probability that the balls chosen from Urn C are 1 white and 1 blue.

Answer 1

A has 3R, 7B

B has 4R, 5W

C has 3W, 6B

after moving 1 from A to B

B has 4.3R, 5W, 0.7B, on avrage

after moving 1 from B to C

C has 0.43R, 3.5W, 6.07B, on average

choosing 2 from resulting C

with replacement is probbility about 21%

without replacement, about 25%