One hundred voters were asked their opinions of two candidates, a and b, running for mayor. their responses to three questions are summarized below number saying yes do you like a? 65 do you like b? 55 do you like both? 25 what is the probability that someone like exactly one given that they like at least one?

Question

Deangelo Chambers

Mathematics

8 December, 10:04

One hundred voters were asked their opinions of two candidates, a and b, running for mayor. their responses to three questions are summarized below number saying yes do you like a? 65 do you like b? 55 do you like both? 25 what is the probability that someone like exactly one given that they like at least one?

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Aidan Wells · Answer 1

I would be interested to hear from others here, but first if you draw a venn diagram with two circles, label them A and B for candidates A and B, the intersection will be 25 (i. e. number of voters that like both candidates. that means A/B will be 40 (only voted for A) and B/A will be 30 (only voted for B). Of course, 40 + 30 + 25 only equals 95, and there were 100 voters, which means 5 did not vote for either candidate. So that 5 will be outside set A and B. The "At Least" question normally implies the probability axiom P (not E) = 1 - P (E).