Assume that 1 out of 100 fighters observed on a radar are from enemies flying ov

Question

Assume that 1 out of 100 fighters observed on a radar are from enemies flying over a war zone. A friend-foe detection system of three radars are used to detect the targets. Each radar has a probability of detection of 90% and false alarm rate of 5%. The system uses a majority rule, i.e., if the system determines there is a target (no target) when the majority of the radars determines there is a target (no target). (a) Find the probability of detection of the system. (b) Find the false alarm rate of the system.

Explanation / Answer

a) Probability of detection = P(at least 2 out of 3 correct detections)

= 3 x 0.9x0.9x0.1 + 0.9x0.9x0.9

= 0.972

b) False alarm rate = P(2 or more false alarms)

= 3x0.05x0.05x0.95 + 0.05x0.05x0.05

= 0.00725

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