Mysterious Transfer. Of two bags, one contains four white balls and three black balls and the other contains three white balls and five black balls. One ball is randomly selected from the first bag...

Mysterious Transfer. Of two bags, one contains four white balls and three black balls and the other contains three white balls and five black balls. One ball is randomly selected from the first bag and placed unseen in the second bag.

(a) What is the probability that a ball now drawn from the second bag will be black?

(b) If the second ball is black, what is the probability that a black ball was transferred?