Question

According to a poll, 30% of voters support a ballot initiative. Hans randomly surveys 5 voters. What is the probability that exactly 2 voters will be in favor of the ballot initiative? Round the answer to the nearest thousandth.

Answer 1

Use binomial distribution, p=0.3 = constant
n=5 (sample size)
x=2 (desired outcome)
Probability of x=2 out of sample size of n=5 is
\(P(X=x)=C(n,x)p^x(1-p)^{n-x}\)
where
\(C(n,x)=n!/(x!(n-x)!)\)

Plug in numbers and solve for porbability P(X=2).

For more examples and background, see for example:
http://www.euclid.host-ed.me/probability/binomialDistribution.html