Let X the number of times, he hits the targets. Hitting the target is a Bernoulli trial, So, X has a binomial distribution. ∴ P(X=x)=nCxqn−xpx where, n= Number of times hit p= probability of hitting =
2
3
q= probability of not hitting =1−
2
3
=
1
3
∴ P(X=x)=nCx(
1
3
)n−x(
2
3
)x Given,P(x≥1)>90% ∴ 1−P(X=0)>90% 1−nC0(
1
3
)n(
2
3
)0>0.9 1−(
1
3
)n>0.9⇒0.1>(
1
3
)n ⇒ 3
1
2
>10 ⇒n≥3 ∴ Minimum number of times to hit the target =3