A sensor is used to monitor the performance of a nuclear reactor. The sensor accu-rately reflects the state of the reactor with a probability of .97. But with a probabilityof .02, it gives a false alarm (by reporting excessive radiation even though the reac-tor is performing normally), and with a probability of .01, it misses excessive radia-tion (by failing to report excessive radiation even though the reactor is performing abnormally). (a) What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?

The probability of an incorrect report is found to be 0.03 or 3%.

Explanation:

We will get an incorrect report in both the cases of false alarm or missing excessive radiation. Since, both are mutually exclusive events. Therefore, the probability of both events to occur simultaneously will be 0. Thus, the probability of an incorrect report will be the sum of the probability of false alarm and the probability of a missing radiation.

P (False Alarm) = 0.02

P (Missing Radiation) = 0.01

P(Incorrect Report) = P (False Alarm) + P(Missing Radiation)

P (Incorrect Report) = 0.02 +0.01

P(Incorrect Report) = 0.03 = 3%

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