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  3. A telephone system has n telephone lines. For each of the n lines, the event that the line will fail during a certain reliabilit

A telephone system has n telephone lines. For each of the n lines, the event that the line will fail during a certain reliabilit

admin2020-05-11  26
问题 A telephone system has n telephone lines. For each of the n lines, the event that the line will fail during a certain reliability test has probability 0.3, and these n events are independent. If the probability that at least one of the n lines will not fail during the reliability test is greater than 0.99, what is the minimum value of n?
选项 A、2
B、3
C、4
D、5
E、6
答案C
解析 一次失败的概率是0.3，则一次成功的概率是0.7。
P(至少一次不失败)=1-P(每次都失败)=1-0.3n＞0.99
0.3n＜0.01
通过试数可得出n最小为4，所以选C。
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