UPSC NDA I 2015 Mathematics Solved Paper

We know that the mean and variance of a binomial distribution with number of trials as ‘n’ and the probability of success as ‘p’ are
Mean = np
Variance = np(1-p)
Therefore applying the given conditions yields us
np=2
np(1−p)=1
2(1−p)=1
1−p=

1

2

p=

1

2

Therefore the number of trials will be 4
P(X=0)
=4C0(1−P)4
=

1

24

=

1

16