UPSC NDA I 2025 Mathematics Paper

Given,
Let X be a random variable following a binomial distribution with parameters n=6 and p=‌

1

4

The probability mass function for a binomial distribution is:
P(X=x)=(

n

x

)px(1−p)n−x
For P(X=3), we have:
P(X=3)=(

6

3

)(‌

1

4

)3(‌

3

4

)3
Substitute the values:
P(X=3)=20×‌

1

64

×‌

27

64

Now simplify the equation:
P(X=3)=20×‌

27

4096

=‌

540

4096

Simplifying the fraction:
P(X=3)=‌

135

1024