Question

The probability that a single radar station will detect an enemy plane is 0.65.

(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?
stations

(b) If four stations are in use, what is the expected number of stations that will detect an enemy plane? (Round your answer to one decimal place.)
stations

Answer 1

(A) It is given that p = 0.65 (detecting the energy plane)

Probability of not detecting the enemy plane = 1 - p = 1-0.65 = 0.35

Probability that none of n stations to detect an energy plane =

So, P(detecting at least 1 energy plane) = 1 - P(detecting 0 energy plane)

= 1-

we want this probability to be 98% or 0.98

So, we can write

0.98 = 1 -

solving for n, we get

= 1-0.98

or = 0.02

this gives n = 3.73

rounding to nearest integer, we get n = 4 stations

So, answer is 4 planes

(B) Expected value = n*p

we have n = 4 and p = 0.65

this implies

Expected value = 4*0.65 = 2.6