Chapter 8.3, Problem 60E

Problems $59\text{-}62$ refer to the following experiment: $2$ balls are drawn in succession out of a box containing $2$ red and $5$ white balls. Let $R_i$, be the event that the $ith$ ball is red, and let $W_i$, be the event that the $ith$ ball is white.

Find the probability that the second ball was red, given that the first ball was

(A) Replaced before the second draw

(B) Not replaced before the second draw