UPSC NDA Math Model Paper 1

Variable X has a binomial distribution B(6,

1

2

).
∴n=6 and p=

1

2

And, 1−p=1−

1

2

=

1

2

=p.
For a random variable X, the probability is given by P(X=k)=‌nCkpk(1−p)n−k.
∴P(X=k)=‌6Ckpkp6−k
=‌6Ckp6
=‌6Ck(

1

2

)6
Now, the most likely outcome will be when P(X=k) will be maximum for k=0,1,2,3,4,5 or 6.
⇒‌6Ck(

1

2

)6 is maximum.
⇒‌6Ck is maximum.
⇒k=

6

2

=3
∴ The most likely outcome is when the value of X=k=3.