For an urn with balls labeled 1, 2, 3, . . . , 10. To balls are drawn from the urn. Let X1 be the number on the first ball and X2 be the number on the second ball drawn. By counting the favorable outcome, compute the following probabilities P(X1 = 7) P(X1 = 8) P(X1 = 7, X2 = 8) in the cases a) and b).

a) The balls are drawn with replacement.

b) The balls are drawn without replacement.

c) Does the answer to either a) or b) prove the independence of the random variables X1 and X2?