Question

n 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 59% 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 voted in the last presidential election?

Answer 1

Part 2 The voter did not vote in the last presidential election?

Answer 2

So, let
\(D\) = has a college degree
\(\overline{D}\) = does not have a college degree
\(V\) = voted in the last election
\( \overline{V}\) = did not vote in the last election

You're given:
\(P(D)=200/1000 = 0.2\)
\(P(V|D) = 0.7\)
\(P(V|\overline{D})=0.59\)

1st: They ask you to find \(P(V)\)
Observe that \(P(V) = P(V \cap D)+ P(V \cap \overline{D})\) by the law of total probability
From the condition probabilities you are given, you determine:
\[P(V|D)= \frac{P(V \cap D)}{P(D)} \implies P(V \cap D)=P(V|D)P(D)=0.7(0.2)=0.14\]
Similarly
\[ P(V|\overline{D})=P(V|\overline{D})P(\overline{D})=0.59(1-0.2)=0.472\]

So, \(P(V) = 0.14 + 0.472 = 0.612\)

Answer 3

the 2nd question is then very easy
You are asked to find \(P(\overline{V})\)... and \(P(\overline{V})=1-P(V)\) and that's it

Answer 4

oh okay thank you

Answer 5

:) yw

Answer 6

i'm still having trouble with the second question

Answer 7

it's just \(1 - 0.612\)

Answer 8

=0.388

Answer 9

I am making this problems so much harder than what they are. Thank you so much.