Question #16 / 20 Recently, Hector ran for president of the local school board.

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Question #16 / 20 Recently, Hector ran for president of the local school board. Of those who voted in the election, 90% had a high school diploma, and the other 10% did not. Hector got 65% of the vote of those with high school diplomas, while he got only 40% of the vote of those without high school diplomas Let D denote the event that a randomly chosen voter (in the school board election) had a high school diploma and D denote the event that a randomly chosen voter did not have a high school diploma. Let H denote the event that a randomly chosen voter voted for Hector and H denote the event that a randomly chosen voter did not vote for Hector Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses P(D0.65 r(D) = 0.4 P(D) = 0.1 P(H | D) = What is the probability that a randomly chosen voter voted for Hector? Clear Undo Help

Explanation / Answer

P(D) = 0.9

P(D') = 0.1

P(H|D) = 0.65

P(H|D') = 0.4

So, P(H) = If voter has diploma and voted for Hector or if voter does not have diploma and voted for Hector

= P(H|D).p(D) + p(H|D').p(D') = 0.9*0.65 + 0.1*0.4 = 0.625 is the required probability

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