Question

If an aircraft is present in a certain area, a radar correctly registers its presence with probability 0.99. if it is not present, the radar falsely registers an aircraft presence with probability 0.10. we assume that an aircraft is present with probability 0.05. what is the probability of false alarm (a false indication of aircraft presence), and the probability of missed detection (notng registers, even though an aircraft is present)? what is the probability that an aircraft is present given that the radar registers a presence?

Answer 1

the probability of false alarm = 0.95 x 0.1
                                             
                                              = 0.095


the probability of missed detection = 0.05x0.01

                                                        = 0.0005

the probability that an aircraft is present given that the radar registers a presence

                                                         = 0.05x0.99

                                                         = 0.0495

NOTE

See the attached image for the tree diagram.

Answer 2

Step-by-step explanation:

A = {an aircraft is present },

B = {t he radar generates an alarm} ,

and their compliments

A'' = {an aircraft is not present },

B'' = {the radar does not generate an alarm } .

P ( not present , false alarm) = P (A''  n B) = P ( A'' ) P ( B l A'') = 0.95 · 0. 1 0 = 0.095,

P ( present , no detection ) = P (A n B'' ) = P ( A ) P ( B'' I A) = 0.05 · 0 . 01 = 0.0005.