I can't figure out how to find out following problem probability. I am in stuck but it is very important for me. Here is the problem description.
Box one contains $3$ white balls and $7$ black balls.
Box two contains $6$ white balls and $4$ black balls.
If the first ball is white, we then randomly pick the second ball from box one. If the first ball is black, we randomly pick second ball from box 2.
1) What is the probability that the second ball is white?
2) Given that the second ball is white. What is the probability that the second ball is picked from box two?