Assume 60p6 of the people in a community use the emergency a

Assume 60%(p=.6) of the people in a community use the emergency at a hospital in a year. If you randomly choose 12 people from the community: What is the probability that exactly 6 used the emergency room?

Solution

Given X follows Binomial distribution with n=12 and p=0.6

P(X=x)=12Cx*(0.6^x)*(0.4^(12-x)) for x=0,1,2,...12

So the probability is

P(X=6) = 12C6*(0.6^6)*(0.4^(12-6)) =0.1765791