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(2014 · anqing simulation) in three independent repeated tests, the probability of event a occurring in each test is the same. If the probability of event a occurring at least once is 6364, the probability of event a occurring just once is () A. 14B. 34C. 964D. 2764
Suppose that the probability of event a occurring in one test is p, then the probability of event a not occurring in one test is 1-p. the opposite event of event a occurring at least once in three independent tests is "event a does not occur once in three independent tests", that is, (1-p) 3 = 1-6364, the solution can be obtained, P = 34, and the probability of event a occurring just once is p = C31 × 34 × (1-34) 2 = 964; so select C
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