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An urn contains 4 black balls and 5 white balls. After a thorough mixing, a ball is drawn from…

 An urn contains 4 black balls and 5 white balls. After a thorough mixing, a ball is drawn from the urn, its color is noted, and the ball is returned to the urn. (a) What is the probability that 5 black balls are observed in 15 such draws? (b) What is the probability that 15 draws are required until the first black ball is observed? (c) What is the probability that 15 draws are required until the fifth black ball is observed?