Question

A bag contains blue and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a blue marble and then a yellow marble is 0.37, and the probability of selecting a blue marble on the first draw is 0.55.

What is the probability of selecting a yellow marble on the second draw, if the first marble drawn was blue?

Answer 1

Let A be the event that you draw a blue marble on the first draw.
Let B be the event that you draw a yellow marble on the second draw.

P(A) = .55
P(AB) = .37 = P(BA)

We want the conditional probability B given A, P(B|A) = P(BA)/P(A)
P(B|A) = P(BA)/P(A) = .37/.55 ~= .673