Question

Question 1

Recently, Hector ran for president of the local school board. Of those who voted in the election,

80%

had a high school diploma, and the other

20%

did not. Hector got

55%

of the vote of those with high school diplomas, while he got only

20%

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.

(If necessary, consult a list of formulas.)

					=PHD
								=P∩DH
	=PD	0.8
								=P∩DH
					=PHD	0.45
					=PHD
								=P∩DH
	=PD
								=P∩DH
					=PHD	0.8
What is the probability that a randomly chosen voter voted for Hector?

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Answer 1

As per the given problem H and D are not clear as they got displayed two times for two different events.

For the answer probability that randomly chosen water voted for Hector can be calculated as below:

Let 100 students are there who have given their vote.

So out of 100, 80 are from high school and 20 are from non-high school.

Out of which 55% of vote from high scholl so total studen who had voted for Hector is 44 (55*0.8)

Out of which 20% of vote from without high scholl so total studen who had voted for Hector is 4 (20*0.2)

So out of 100 students 48 voted for the Hectore and 52 voted for else.

So if we choose the random sample, we will have 48 % chnace or 0.48 probability that viter voted for Hectore.