Suppose you will draw 3 marbles without replacement from each of four bags. Bag 1 has 3 red marbles and 6 black marbles; bag 2 has 10 red marbles and 20 black marbles; bag 3 has 500 red marbles and 1000 black marbles; and bag 4 has an infinite number of marbles, but twice as many black marbles as red. Let X1, X2, and X3 be the numbers of red marbles drawn from bag 1, bag 2, and bag 3, respectively, and let Y be the number of red marbles drawn from bag 4.
(a) What is the probability distribution of Y ?
(b) Make the following table and fill in all the probabilities: x 0 1 2 3
P(X1 = x)
P(X2 = x)
P(X3 = x)
P(Y = x)
(c) Explain what you think is the point of this question
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