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A fair die is thrown twice and the number on the upturned face is observed each time. (a) Let be the event that the sum

A fair die is thrown twice and the number on the upturned face is observed each time.

(a) Let be the event that the sum of the two numbers is 6 and let be the event that the second number is even. Are A and B independent? Explain.

(b) Calculate the probability that the second throw produces a bigger number than the first throw.

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