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

In a survey of 1000 eligible voters selected at random, it was found that 200 had a college degree. Additionally, it was found that 70% of those who had a college degree voted in the last presidential election, whereas 54% 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. 0.14 Correct: Your answer is correct.

(b) The voter did not have a college degree and did not vote in the last presidential election. .432 Incorrect: Your answer is incorrect.

(d) The voter did not vote in the last presidential election.

Solutions

Expert Solution

P(had a college degree) = 200 / 1000 = 0.2

P(voted in last election | had a college degree) = 0.7

P(voted in last election | didn't have a college degree) = 0.54

a) P(had a college degree and voted in the last presidential election) = P(voted in last election | had a college degree) * P(had a college degree) = 0.7 * 0.2 = 0.14

b) P(didn't vote in last election | didn't have a college degree) = 1 - P(voted in last election | didn't have a college degree) = 1 - 0.54 = 0.46

P(did not have a college degree and did not vote in the last presidential election) = P(didn't vote in last election | didn't have a college degree) * P(didn't have a college degree) = 0.46 * (1 - 0.2) = 0.368

c) P(voted in last presidential election) = P(voted in last election | had a college degree) * P(had a college degree) + P(didn't have a college degree)

= 0.7 * 0.2 + 0.54 * (1 - 0.2)

= 0.572

d) P(didn't vote in last presidential election) = 1 - P(voted in last presidential election) = 1 - 0.572 = 0.428

orchestra answered 1 year ago

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