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 90% of those who had a college degree voted in the last presidential election, whereas 50% 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

Here P(College degree) =Total favourable casess/total cases = 200/1000= 0.2

And P( last presidential election ) =0.9

So P( college degree and voted in last presidential election ) = P(college degree) x P( last presi. electiion)

=0.9 x0.2 = 0.180

that is the answer of part (a)

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P(Not college student and not voted in lat presidential election) = n(E)/n(S)

=(800 x 50%)/1000= 400/1000 = 0.400

This is the answer of part (b)

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Now total degree holder who voted + total non degree holder who voted

= 180 + 800 x 50% = 180+400 = 580

So total perons who voted = 580

Thus P( voted )= 580/1000 = 0.580

This is the answer of part (c)

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P(Not voted ) =11- P(voted ) = 1- 0.580 = 0.420

This is the answer of part (d)

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