Question

In a large state, 50% of the eligible voters are democrats, 45% of the eligible voters are republicans, and 5% of the eligible voters are independents. The voter turnouts for a particular election for the three groups are 40%, 55%, and 65% respectively. (a) find the probability that an eligible voter in this state votes. (b) find the probability that someone who voted in the election is a democrat.

Answer 1

Let A=event that a voter is a democrat, B= event that voter is republican, C= voter is independent

P(A)=0.5, P(B)=0.45, P(C)=0.05

Let D: the voter is eligible or an eligible voter votes

Given P(D|A)=0.4, P(D|B)=0.55, P(D|C)=0.65

a) Probability that an eligible voter in the state votes = P(D)

=P(D|A)*P(A) + P(D|B)*P(B) + P(D|C)*P(C)

=0.4*0.5 + 0.55*0.45 + 0.65*0.05

=0.48

b) Probability that someone who voted is democrat

=P(A|D) = P(D|A)*P(A) /P(D) (by Bayes theorem)

=0.4*0.5 / 0.48

=0.4167