Please help with all parts of the problem In a certain town

In a certain town. 41.6% of the voters arc Democrats and 58.4% of the voter are Republicans. In the last election 32.6% of the Democrats. and 37.7% of the Republicans voted. If a citizen who is a Republican is randomly selected, what is the probability that they voted in the last election? If a citizen who did not vote in the last election is randomly selected. what is the probability that they are a Democrat?

Solution

Let

R = republican
D = democrat
V = voted

a)

As given already,

P(V|R) = 0.377 [ANSWER]

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b)

P(D|V\') = P(D) P(V\'|D) / P(V\')

As

P(V\') = P(D) P(V\'|D) + P(R) P(V\'|R)

= 0.416*(1-0.326) + 0.584*(1-0.377)

P(V\') = 0.644216

Thus,

P(D|V\') = P(D) P(V\'|D) / P(V\') = 0.416*(1-0.326)/0.644216

= 0.435232903 [ANSWER]