In a survey of 1000 eligible voters selected at random, it was found that 200 ha

Question

In a survey of 1000 eligible voters selected at random, it was found that 200 had a college degree. Additionally, it was found that 80% of those who had a college degree voted in the last presidential election, whereas 45% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random will have the following characteristics. (Round your answers to three decimal places.) (a) The voter had a college degree and voted in the last presidential election. (b) The voter did not have a college degree and did not vote in the last presidential election. (c) The voter voted in the last presidential election. (d) The voter did not vote in the last presidential election.

Explanation / Answer

P(College Degree) = 200/1000 = 0.2

P(No college degree) = 1 - 0.2 = 0.8

P(Voted| College degree) = 0.80

P(Voted| No College degree) = 0.45

Hence,

a) P(Voted and college degree) = P(Voted|College degree)*P(College degree) = 0.80*0.20 = 0.16

b) P(No College degree and no vote) = P(Not voted| No College degree)*P(No College degree) = (1-0.45)*0.80 = 0.44

c) P(Voted) = 0.20*0.80 + 0.80*0.45 = 0.52

d) P(Did not vote) = 1 - 0.52 = 0.48

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