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  3. Consider an experiment with events A and B The probability of event A is 0.63, a

Consider an experiment with events A and B The probability of event A is 0.63, a

游客2024-01-12  21
问题 Consider an experiment with events A and B The probability of event A is 0.63, and the probability of event B is 0.58. What is the least possible probability when both event A and B happen? ________.
选项
答案 0.21
解析 由P(A or B)=P(A)+P(B)-P(A and B)，可知P(A and B)=P(A)+P(B)-P(A or B)，想让其最小，则应该让P(A or B)最大，而在同一个概率实验下，A或B发生的最大值等于1，于是P(A and B)=P(A)+P(B)-P(A or B)=0.63+0.58-1=0.21。大家容易想到A和B交集最小就是A和B互斥，但若A和B互斥，两个集合的对应的概率相加就会超过1，与实际不符。
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