A population of voters contains 40 republicans and 60 Democr

A population of voters contains 40% republicans and 60% Democrats. It is reported that 30% of the republican and 70% of the Democrats favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional proability that this person is a Democrat.

Solution

Let

F = favor
D, R = democrat, republican

As

P(F) = P(D) P(F|D) + P(R) P(F|R) = 0.60*0.70 + 0.40*0.30 = 0.54

Hence,

P(D|F) = P(D) P(F|D) / P(F) = 0.60*0.70/0.54 = 0.777777778 [ANSWER]