An urn contains 5 white and 4 black balls Four balls are tra

An urn contains 5 white and 4 black balls. Four balls are transferred to a second urn. A ball is then drawn from this second urn, and it happens to be black. Find the probability of drawing a white ball from the remaining three balls in the second urn. The answer is .625, but I do not know how to get that answer.

Solution

Since we do not know the color of 3 balls of the other bag, those 3 balls can be any 3 of 5 white and 3 black balls. When we pick one ball at random from these 3 balls, it is same as picking any one ball at random from a bag containing 5 white and 3 black balls. Thus probability of getting a white ball = 5/8 = 0.625