Suppose box 1 contains 2 white balls and 1 black ball, box II contains 1
white ball and 3 black balls, and box III contains 2 white balls and 2 black
balls. (15%)
(a) One ball is selected from each box. Calculate the probability of getting
all white balls. (5%)
(b) One box is selected at random and one ball is drawn from it. Calculate
the probability that it will be white. (5%)
(c) In (b), calculate the probability that the first box was selected given that
a white ball is drawn. (5%)
(a) Determine the constant c so that it satisfies the property of joint
probability density function. (5%)
(b) Are the random variables X and Y dependent? Give the reason for
your answer. (5%)
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