Suppose 60% of all college professors like tennis, 65% like bridge, and 50% like chess; 45% like any given pair of recreations. (a) should you be suspicious if told 20% like all three recreations?

Let T represent tennis, B represent bridge and C represent chess.

Suppose it is true that 20% of all college professors like all three recreations, then



Because the union of all probability is not 1, this is not a valid distribution and hence, we would be suspicious.

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The answer is