Question

Example 5

A committee of 11 members is voting on a proposal. Each member casts a yea or nay vote. On
a random voting basis, what is the probability that the final vote count is unanimous?

Answer 1

Let X be the number of "no" votes. Suppose that a "yes" or "no" is equally likely. Then, X is a binomial random variable with probability p = 1/2 and n = 11 trials.

i.e. X ~ Binomal (1/2,11).

Then,

`P(X=3)=((11)/(3) )((1)/(2) )^(3) ((1)/(2))^(8) =8.05`%