Probability Theory

Suppose two balls are drawn sequentially without replacement from an urn containing r red and b black balls. The probability of getting a red ball on the first draw is r/(r b). If, however, one is told that a red ball was obtained on the first draw, the conditional probability of getting a red ball on the second draw is (r - 1)/(r b - 1), because for the second draw there are r b - 1 balls in the urn, of which