Math Help - Bags with balls.

1. Bags with balls.

One bag contains 6 white balls and 4 black balls, and a second bag contains 5 white balls and 4 black balls. One ball is drawn out at random from the first bag and is placed unseen in the second bag.

a. What is the probability that a ball now drawn from the second bag is black?

b. If the ball from the second bag is black, what is the probability that the ball from the first bag was white?

Could some one show me how to work out this problem I'm having a tough time with it.
I have the answer just need to know how to work it out.
A.) 11/25
B.) 6/11

thanks

2. Part A
$\begin{array}{rcl}
{P(B_2 )} & = & {P(W_1 B_2 ) + P(B_1 B_2 )} \\
{} & = & {P(B_2 |W_1 )P(W_1 ) + P(B_2 |B_1 )P(B_1 )} \\ \end{array}$