Chapter 1.5, Problem 1E

Bowl B1 contains two white chips, bowl B2 contains two red chips, bowl B3 contains two white and two red chips, and bowl B4 contains three white chips and one red chip. The probabilities of selecting howl B1, B2, B3, or B4 are $\frac{1}{2},\frac{1}{4},\frac{1}{8}$, and $\frac{1}{8}$, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find

(a) $P\left(W\right)$, the probability of drawing a white chip.

(b) $P\left(B_1|W\right)$, the conditional probability that bowl B1 had been selected, given that a white chip was drawn.