# Math Help - Probability of radar falsely registering aircraft

1. ## Probability of radar falsely registering aircraft

Aircraft is in certain area, radar correctly registers its presence with prob. of 0.95. If it is not present, radar falsely registers its presence with prob. of 0.03. We assume that aircraft is present with prob of 0.1.

So P(aircraft is present)= 0.1 and P(radar registers an aircraft) = 0.95 correct??
Because I cannot figure out how to start on the questions below..

Probability of false alarm
Probability of missed detection
Probability that an aircraft is present if not registered (conditional probability right?)

guidance is appreciated!!

2. Originally Posted by mightydog78
Aircraft is in certain area, radar correctly registers its presence with prob. of 0.95. If it is not present, radar falsely registers its presence with prob. of 0.03. We assume that aircraft is present with prob of 0.1.

So P(aircraft is present)= 0.1 and P(radar registers an aircraft) = 0.95 correct??
Because I cannot figure out how to start on the questions below..

Probability of false alarm
Probability of missed detection
Probability that an aircraft is present if not registered (conditional probability right?)

guidance is appreciated!!
Pr(radar registers aircraft | aircraft present) = 0.95.

Pr(radar registers aircraft | aircraft not present) = 0.03.

Pr(aircraft present) = 0.1.

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Probability of false alarm = Pr(radar registers aircraft | aircraft not present) = 0.03.

Probability of missed detection = Pr(radar does NOT register aircraft | aircraft present) = ....

Probability that an aircraft is present if not registered = Pr(aircraft present | radar does NOT register aircraft) = ....

3. You need to use Bayes' Theorem. You can find it on wikipedia

First find the probability of $r$

Then find the probability of $(r'|p)$

Then use Bayes' Theorem to find $(p|r')$

Bayes' Theorem formula:

$pr(a|b)=\frac{pr(b|a)*pr(b)}{pr(a)}$

If you need more help, feel free to ask.