14\" (Voters) The registered voters in a certain district break down as follows:

Question

14" (Voters) The registered voters in a certain district break down as follows: 45% Democrats, 42% Republicans, and 13% Independents. In a certain election, 22% of the Democrats, 25% of the Republicans, and 83% of the Independents voted in favor of a proposition. Determine the probability that a randomly chosen voter: (b) Voted in favor of the proposition (a) Is an Independent. (c) Is an Independent, if the individual voted in favor of the proposition. (d) Not a Democrat, given that the individual did not vote in favor of the proposition.

Explanation / Answer

a) P(independent) = 0.13

b) P(voted in favor of the proposition) = 0.45x0.22 + 0.42x0.25 + 0.13x0.83

= 0.3199

c) P(independent | voted in favor of proposition) = 0.13x0.83/0.3199

= 0.3373

d) P(not a democrat | did not vote for proposition) = [0.42x(1-0.25)+0.13(1-0.83) ]/ [0.45x(1-0.22)+0.42x(1-0.25)+0.13(1-0.83) ]

= 0.3371/0.6881

=0.4899

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