Problem 113E

Consider one of the radar sets of Exercise 2.112. What is the probability that it will correctly detect exactly three aircraft before it fails to detect one, if aircraft arrivals are independent single events occurring at different times?

Reference

Three radar sets, operating independently, are set to detect any aircraft flying through a certain area. Each set has a probability of .02 of failing to detect a plane in its area. If an aircraft enters the area, what is the probability that it

a goes undetected?

b is detected by all three radar sets?

Answer:

Step 1 of 2:

Given,

Three radar sets operating independently. Radars are set to detect any aircraft flying through a certain area.

Probability of failing to detect a plane in its area = 0.02

The claim is to find the probability that it will correctly detect exactly three aircraft before it fails to detect one