2. If an aircraft is present in a certain area, a radar correctly registers its

Question

2. If an aircraft is present in a certain area, a radar correctly registers its presence with probability .96. If it is not present, the radar falsely registers its presence with probability .03. We assume that aircraft is present with probability .2. (6) Use Notation: A (an aircraft is present), B fthe radar registers an aircraft)! a) Find the probability of false alarm. b) Find the probability of missed detection c) Find the probability that an aircraft is present if it is not registered d) Find the probability that an aircraft is not present if it is registered

Explanation / Answer

Ans:

Given that

P(present)=0.2

P(not present)=1-0.2=0.8

a)P(false alarm)=P(registers/not present)=P(B/A')=0.03

b)P(missed detection)=P(not register/present)=P(B'/A)=1-P(B/A)=1-0.96=0.04

c)P(register)=P(register/present)*P(present)+P(register/not present)*P(not present)

=0.96*0.2+0.03*0.8

=0.216

P(not regsiter)=1-0.216=0.784

We have to find:

P(present/not register)=P(not register/present)*P(present)/P(not register)

=0.04*0.2/0.784

=0.0102

d)P(not present/register)=P(register/not present)*P(not present)/P(register)

=0.03*0.8/0.216

=0.1111

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