In a survey of 1000 eligible voters selected at random, it was found that 100 ha

Question

In a survey of 1000 eligible voters selected at random, it was found that 100 had a college degree. Additionally, it was found that 70% of those who had a college degree voted in the last presidential election, whereas 55% 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.)

The voter did not have a college degree and did not vote in the last presidential election.

The voter voted in the last presidential election.

The voter did not vote in the last presidential election.

Explanation / Answer

Let

C= has college degree
V = voted

The voter did not have a college degree and did not vote in the last presidential election.

P(C' n V') = P(C') P(V'|C') = (1-100/1000)*(1-0.55) = 0.405 [ANSWER]

*************************************

The voter voted in the last presidential election.

Also,

P(V) = P(C) P(V|C) + P(C') P(V|C')

= (100/1000)*(0.70) + (1-100/1000)*(0.55)

= 0.565 [ANSWER]

*************************************

The voter did not vote in the last presidential election.

Hence,

P(V') = 1 - P(V) = 1 - 0.565 = 0.435 [ANSWER]

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