The probability that a voting-age adult in 2004 voted in the presidential election was 0.57. Five voting-age adults in 2004 were randomly selected. Find the probability that exactly 2 or the 5 adults voted in the presidential election.

Answer 1

prob(voting) = .57
prob(not voting) = .43

prob(2 of 5 voted)
= C(5,2) (.57)^2 (.43)^3
= .2583

Answer 2

p=probability of voting
q=(1-p)=probability of not voting.

Out of 5 adults randomly selected, the probability that exactly 2 voted is calculated according to the binomial expansion,
C(5,2)p^2q^3
=(5!/(2!3!))*0.57^2*0.43^3
=0.258 (approx.)