Question

Three radar sets are set to detect any aircraft flying through a certain area. Each set has a probability of 0:25 of failing to detect a plane flying through the area. A plane has now entered the designated area.

a. What is the probability the plane passes through detected?

b. Given the plane passed through detected, what is the probability that at least two radar sets successfully detected the plane?

Answer 1

Assuming the radars operate independently

a. )

Probability that the plane is not detected by all three radars = P( ) = ( 0.25)^3

Therefore,

Probability the plane passes through detected = P( A) = 1- ( 0.25)^3 = 0.984375

b)

Conditional probability that a plane was detected by the radar set A, given that it was detected (by any of A, B or C)

= = = 0.253968