Two fair dice are thrown. Let E7 denote the event that the sum of the dice is

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Two fair dice are thrown. Let E7 denote the event that the sum of the dice is 7. Let F denote the event that the first die equals 4 and let T be the event that the second die equals 3. Now it can be shown (see Problem 36) that E7 is independent of F and that E7 is also independent of T; but clearly E7 is not independent of FT [since P(E7|FT ) = 1].

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