2. 外语
  3. Suppose that you roll the weighted 6-sided die from example 4.4.5 twice. What is the probability that the first roll will be an

Suppose that you roll the weighted 6-sided die from example 4.4.5 twice. What is the probability that the first roll will be an

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问题 Suppose that you roll the weighted 6-sided die from example 4.4.5 twice. What is the probability that the first roll will be an odd number and the second roll will be an even number?
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答案12/49
解析 To calculate the probability that the first roll will be odd and the second roll will be even, note that these two events are independent. To calculate the probability that both occur, you must multiply the probabilities of the two independent events. First compute the individual probabilities.
P(odd)= P(l)+ P(3)+ P(5)=3/7
P(even)= P(2)+ P(4)+ P(6)= 4/7
Then, P(first roll is odd and second roll is even)= P(odd)P(even)=
Two events that happen sequentially are not always independent. The occurrence of one event may affect the occurrence of a following event. In that case, the probability that both events happen is equal to the probability that the first event happens multiplied by the probability that given that the first event has already happened, the second event happens as well.
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