Bowl B₁ contains two white chips, bowl B₂ contains two red chips, bowl B₃ contains two white chips and two red chips, and bowl B₄ contains three white chips and one red chip. The probabilities of selecting bowl B₁, B₂, B₃, or B₄ are 1/2, 1/4, 1/8 and 1/8, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find:
(a) P (W), the probability of drawing a white chip.
(b) P (B₁ Given W), the conditional probability that bowl B₁ had been selected, given that a white chip was drawn.