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Three radar sets, operating independently, are set to detect any aircraft flying through a certain area....

Three radar sets, operating independently, are set to detect any aircraft
flying through a certain area. Each set has a probability of 0.04 of
failing to detect a plane in its area.
Consider one of the radar sets. What is the probability that it will
correctly detect exactly three aircraft before it fails to detect one, if
aircraft arrivals are independent single events occurring at different
times? (Round your answer to four decimal places.)

math   Statistics-And-Probability   
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Answer #1

probability that it will
correctly detect exactly three aircraft before it fails to detect one

=P(three success and then one failure) =(1-0.04)^3*0.04 =0.0354

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