2. 外语
  3. Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rollin

Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rollin

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问题 Suppose that there is a 6-sided die that is weighted in such a way that each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 5 are all equal, but the probability of rolling a 6 is twice the probability of rolling a 1. When you roll the die once, the 6 outcomes are not equally likely. What are the probabilities of the 6 outcomes?
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答案2/7
解析 Using the notation P(l)for the probability of rolling a 1, let p = P(l). Then each of the probabilities of rolling a 2, 3, 4, or 5 is equal to p, and the probability of rolling a 6 is 2p. Therefore, since the sum of the probabilities of all possible outcomes is 1, it follows that
1 = P(l)+ P(2)+ P(3)+ P(4)+ P(5)+ P(6)=p +p +p+p+p + 2p
= 7p
So the probability of rolling each of the numbers from 1 to 5 is p =1/7, and the probability of rolling a 6 is 2/7.
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