A bag contain 4 whites and 6 blacks balls Two balls are draw

A bag contain 4 whites and 6 blacks balls. Two balls are drawn in succesion at random and this process is made two times. What is the probability that one is black and the other white?

Solution

There are two cases:

1. Black then white
2. white then black

Thus, by Bayes\' rule,

P(black and white) = P(black first) P(white|given black first) + P(white first) P(black|white first)

Thus,

P(black and white) = (6/10)(4/9) + (4/10)(6/9) = 8/15 or 0.533333 [ANSWER]