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

Complete 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?

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

a

b

Step-by-step explanation:

From the question we are told that

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

 Gnerally the probability that an enemy plane flying over will be detected by at least one station is mathematically represented as

=>  

=>       Note

=>  

=>  

Generally from binomial probability distribution function

Here C represents combination hence we will be making use of of combination functionality in our  calculators

Generally any number combination 0  is  1

So  

=>  

taking log of both sides

=>  

=>  

=>  

=>  

=>    

Gnerally the expected number of stations that will detect an enemy plane is  

=>

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x