6 Sixty percent of the eligible voting residents of a certai

6. Sixty percent of the eligible voting residents of a certain community support the incumbent        candidate. If eight of the residents are selected at random, find the probability that at least five of the eight support the candidate.

Solution

Given X follows Binomial distribution with n=8 and p=0.6

P(X=x)=8Cx*(0.6^x)*(0.4^(8-x)) for x=0,1,,2...,8

So the probability that at least five of the eight support the candidate is

P(X>=5) = P(X=5)+P(X=6)+P(X=7)+P(X=8)

=8C5*(0.6^5)*(0.4^(8-5))+...+8C8*(0.6^8)*(0.4^(8-8))

=0.5940864