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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 :

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,

[tex]P(X=3)=(\frac{11}{3} )(\frac{1}{2} )^{3} (\frac{1}{2})^{8} =8.05[/tex]%

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