A total of 600 of the 1,000 people living in a retirement community classify themselves as Republicans, while the others classify themselves as Democrats. In a local election in which everyone voted, 60 Republicans voted for the Democratic candidate, and 50 Democrats voted for the Republican candidate. If a randomly chosen community member voted for the Republican, what is the probability that she or he is a Democrat?

Question

Mathematics

Rocco Frost

10 May, 00:23

A total of 600 of the 1,000 people living in a retirement community classify themselves as Republicans, while the others classify themselves as Democrats. In a local election in which everyone voted, 60 Republicans voted for the Democratic candidate, and 50 Democrats voted for the Republican candidate. If a randomly chosen community member voted for the Republican, what is the probability that she or he is a Democrat?

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Answers (1)

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Cannon Gallagher · Answer 1

0.0847 = 8.47%

Step-by-step explanation:

Since 600 people are classified as Republicans, 400 people are classified as Democrats.

It can be calculated the number of people who voted for each party as follows:

Votes for Republicans = 600 (total Republicans) - 60 (Republicans who voted for the Democratic candidate) + 50 (Democrats who voted for the Republican candidate) = 590 votes

Votes for Democrats = 400 (total Democrats) - 50 (Democrats who voted for the Republican candidate) + 60 (Republicans who voted for the Democratic candidate) = 410 votes

A total of 590 people voted for the Republicans and 50 of those are Democrats. Thus, the probability that a person who voted for The Republican candidate is a Democrat can be calulated:

P = 50/590 = 0.0847 = 8.47%