Question

The probability that a single radar set will detect an enemy plane is 0.9. if we have five radar sets, what is the probability that exactly four sets will detect the plane?

Answer 1

The probability that a single radar set will detect an enemy plane is 0.9. if we have five radar sets, what is the probability that exactly four sets will detect the plane?

Solution: The given random experiment follows binomial distribution with
`p=0.9,n=5`

Let x be the number of radar sets that will detect the plane.

We have to find
`P(x=4)`

`P(x=4)=\binom{5}{4}0.9^(4)(1-0.9)^(5-4)`

`=5* 0.6561 * 0.1`

`=0.3281`

Therefore, the probability that exactly four sets will detect the plane is 0.3281