8.19C in statistics 10th edition textbook Witte: A sensor is used to monitor the

Question

8.19C in statistics 10th edition textbook Witte: A sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But what a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive raditation (by failingg to report excessive radiation even though the reactor is performing abnormally).

C.) Being more concerned about failures to detect excessive radiation, someone who live near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radition. (According to this point of view, even a solitary report of a excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?

Explanation / Answer

c) P( excessive radiation will be missed) = (0.01 *0.01) = 0.0001

as both events are independent of each other

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