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Math · Statistics And Probability
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Suppose that a 4-face dice is rolled to determine how a certain amount of prize money is distributed among Student 1, Student 2 and Student 3. If the dice value X is 1, 2 or 3, Student X wins all prize money. If the dice value is 4, each student wins 1/3 of the prize money. Let A be the event that Student i wins nothing. (a) Find the probabilities of the three events Ai, A2 and A3. (b) Find the probabilities of the four events A1A2, A1A3, A2A3 and A1A2A3. (c) Are A1, A2 and A3 pairwise independent (each pair are independent)? (d) Are A1, A2 and A independent?

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