An urn contains six balls: 3 black and 3 red balls. The balls are thoroughly mixed and a ball is drawn from the urn and not replaced. This process is repeated until either 3 red or 3 black ball have been drawn. Let X be the number of draws until we have drawn either 3 red or 3 black balls from the urn.

(a.) Determine ImX, the image of the random variable X.

(b.) Determine P_X(x), the probability mass function of X, and calculate E(X), the expectation of X, and Var(X), the variance of X.

(c.) Use the probability mass function P_X(x) to compute P{X=5|X>=4}.