Problem 2. A radar system tries to detect the presence of enemy airplanes. There

Question

Problem 2. A radar system tries to detect the presence of enemy airplanes. There is a probability p that an
enemy airplane is present, and 1 p that no airplane is present. When an enemy airplane is present, the
probability that something registers (shows up) on the radar screen is q, and there is a 1 q chance that
nothing shows up. When no airplane is present, there is a probability r that something registers on the radar
due to disturbances (noise, birds, etc). What is the false alarm probability? That is, given that something
registers on the radar, what is the probability that there is actually no airplane?

Explanation / Answer

Enemy airplane is present: p

Enemy airplane is not present: 1-p

When enemy airplane is present,

Something shows up: q

Nothing shows up: 1-q

When enemy airplane is not present,

Something shows up: r

Nothing shows up: 1-r

False alarm probability-

P(No air plane/Something Shows up) :

P(Something shows up) = p*q + (1-p)*r

P(No air-plane) = (1-p)

Required probability = (1-p)/(p*q + (1-p)*r)

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