A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans 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 probability that this person is a Democrat.
I tried solving it my way and got the answer of .6. I was wondering if that is correct.. I used P (Democratic | favors issue ) = P ( Democratic and Favors Issue) / P (Favors Issue) which gave me ((.6)(.54)) / (.54) = .6
I have a feeling my calculation and answer is wrong.
$\endgroup$ 31 Answer
$\begingroup$Hint: $$P(R) = 0.4, P(D) = 0.6, P(F\mid R) = 0.3, P(F\mid D) = 0.7 \Rightarrow P(D\mid F)= \dfrac{P(F\mid D)P(D)}{P(F)}= \dfrac{P(F\mid D)P(D)}{P(F\mid D)P(D)+ P(F\mid R)P(R)}=....$$
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