3-50. Vessel A1 contains four white (W) marbles, vessel A2 contains two red (R)

and two white marbles, and vessel A3 contains four red marbles. Suppose P(A1) = 0.5, P(A2) = 0.4, and P(A3) = 0.1 . If a vessel is selected using these probabilities and a marble is drawn at random, find:

(a) The probability of drawing a white marble P(W)

(b) The probability of selecting a red marble P(R)

(c) P(A1|W)

(d) P(A2|R)

(e) P(A1|R)