A box contains n white balls and m blue balls. Balls are drawn at random and with replacement until a blue ball is drawn. What is the probability that (a) exactly n draws are required (b) At least n draws are required.

Here are some hints:

Getting your first blue ball on the nth draw means you had to draw (n-1) whites in a row, followed by the blue. The probability of drawing p white balls in a row is , and the probability of drawing a blue on any one draw is . Can you complete this now?

For the second question, use the fact that the probabiliy of needing at least n draws is one minus the probability of needing lessthan n draws, which in turn is equal to the probability of needing just one draw, plus the probability of needing two draws, plus the probability of needing three draws, etc. up to n.

Post back with what you get for final answers.