Chapter 8.3, Problem 61E

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 at least $1$ ball was red, given that the first ball was

(A) Replaced before the second draw

(B) Not replaced before the second draw