Solutions Probability

A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let:

Question: A box contains four balls, numbered 1 through 4. One ball is selected at random from this box. Let:

X1 = 1 if ball 1 or ball 2 is drawn,

X2 = 1 if ball 1 or ball 3 is drawn,

X3 = 1 if ball 1 or ball 4 is drawn.

The Xi values are zero otherwise. Show that any two of the random variables X1, X2, and X3 are independent but that the three together are not.

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