If a random variable X has a binomial distribution B `(8,1/2)` then find X for which the outcome is the most likely.

Explanation

Given binomial distribution is B `(8.1/2)`
Thus n=8,p=`1/2,q=1/2`
We shall find X which is most likely i.e.for which p(x-r) is maximum where r=0,1,2,.......,8
As p=q, the probability is maximum when `^8C_r` is maximum
But `^8C_r`,r=0,1,2,....... 8 is maximum when r=4.
Thus the most likely outcome is x=4.