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 $P(x=4)$

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

               $=5\times 0.6561 \times 0.1$

               $=0.3281$

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