Question

Currently several radars are used in order to make the system more reliable. If 2 independent radars are installed, where each has a 90% probability of detecting an enemy aircraft
a) What is the probability that at least one of the radars will detect an enemy aircraft entering the area?
b) What is the probability that the plane will pass undetected?

c) What is the probability that the 8th aircraft attempting to cross the area will be the first to do so without being detected?

d) How many attempts do you have to make on average to make an airplane go undetected?

e) How many identical radars are needed so that the probability that an airplane passes undetected is not greater than 0.01%?

Answer 1

A)

probability that at least one of the radars will detect an enemy aircraft entering the area

=1-P(none defect) =1-(1-0.9)^2=0.99

b)

probability that the plane will pass undetected =P(none defect) =(1-0.9)^2=0.01

c)

probability that the 8th aircraft attempting to cross the area will be the first to do so without being detected =P(first 7 gets detected and 8th gets undetected)=0.99⁷*0.01 =0.0093

d)

expected number of attempts =1/p=1/0.01 =100

e)

let number of radars required =a

therefore P(gets undetected) =(1-0.90)^a =0.0001

(1-0.90)^a =0.0001

0.1^a =0.0001

taking log on both sides

a =ln(0.0001)/ln(0.1)= 4