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Numerade Educator

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Problem 14 Medium Difficulty

A committee consists of 1 Democrat, 5 Republicans, and 6 independents. If one person is randomly selected from the committee to be the chairperson, then what is the probability that
a) the person is a Democrat?
b) the person is either a Democrat or a Republican?
c) the person is not a Republican?

Answer

a. $\frac{1}{12}$
b. $=\frac{1}{2}$
c. $\frac{7}{12}$

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Video Transcript

Okay, so we have the following information. And for port, they were asked, What is the probability that the person is a Democrat? So there's one Democrat out of our total, um, amounts of people. So that's five plus 1646 which is 12 to go. So that's one out of 12 report. Be were asked. Um, Paul Body, that's the person is either a Democrats or a Republican. So that's equal to the probability that they're Democrats. Plus the probability that they're Republican, minus the probability that they are both a Democrat and a Republican. So we don't have any Democrat and Republican members. So this probability is just people to go. So we get the probability of a Democrat, which is one out of 12 plus the probability of, ah, Republican, which is five out of 12. So that gives me six over its wall. Okay, No, for part, seeing grass there probability. That's the person is not a Republican, so that means they're either a Democrats or an independent store. That's 1/12 plus 6/12 which is equal to seven over 12