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 [tex]p=0.9,n=5[/tex]
Let x be the number of radar sets that will detect the plane.
We have to find [tex]P(x=4)[/tex]
[tex]P(x=4)=\binom{5}{4}0.9^{4}(1-0.9)^{5-4}[/tex]
[tex]=5\times 0.6561 \times 0.1[/tex]
[tex]=0.3281[/tex]
Therefore, the probability that exactly four sets will detect the plane is 0.3281
