UPSC NDA I 2025 Mathematics Paper

Given,
Probability of hitting the target per shot, p=‌

1

5

Number of shots fired, n=7
The number of hits follows a binomial distribution:
X∼Binomial(n=7,p=‌

1

5

)
Probability of zero hits:
P(X=0)=(‌

4

5

)7
Probability of exactly one hit:
P(X=1)=(

7

1

)(‌

1

5

)(‌

4

5

)6=‌

7

5

(‌

4

5

)6
Probability of at least two hits:
P(X≥2)=1−[P(X=0)+P(X=1)]=1−‌

11

5

(‌

4

5

)6
∴ The probability of hitting the target at least twice is 1−‌

11

5

(‌

4

5

)6.