AP EAPCET 25-Aug-2021 Shift 2 Paper

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