Chapter 8.3, Problem 59E

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.

Construct a probability tree for this experiment and find the probability of each of the events $R_1\cap R_2,R_1\cap W_2,W_1\cap R_2,W_1\cap W_{2,}$, given that the first ball drawn was

(A) Replaced before the second draw

(B) Not replaced before the second draw