Question 1197569: In a recent election there were 1000 eligible voters. They were asked to on two issues, A and B. The results were as follows: 200 people voted for A, 400 people voted for B, and 25 people voted for A and B. If one person is chosen at random from the 1000 eligible voters, find the following probabilities:
1. The person voted for A, given that they voted for B.
Answer:
2. The person voted for B, given that they voted for A.
Answer:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Problem 1
This is what the chart of values looks like
| Voted for A | Did not vote for A | Total | | Voted for B | 25 | 375 | 400 | | Did not vote for B | 175 | 425 | 600 | | Total | 200 | 800 | 1000 |
The phrasing "given they voted for B" means we focus on the "voted for B" row.
We have 400 people who voted for B.
Of this total, 25 also voted for A
25/400 = 1/16
Answer: 1/16
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Problem 2
Refer to the chart in problem 1.
This time we focus on the "voted for A" column since we know 100% the person voted for this candidate.
Of the 200 people who voted for issue A, 25 voted for issue B.
25/200 = 1/8
Answer: 1/8
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