A committee is to consist of 6 members from among 12 people, including Erik. Three of the committee members will be given the titles: president, vice president and secretary. If the committee and the titles are chosen randomly what is the probability that Erik will be the president of the committee?
What is the probability that Erik will be selected as president of the committee?
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probability
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0$6$ members including Erik, or $12$ people including Erik? – 2017-02-09
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0It should be the first – 2017-02-09
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0@barakmanos The way I read this Erik is one of the $12$ people. If the author meant Erik was already a member of the committee, he or she would have written "A committee is to consist of $6$ members, including Erik." There would be no need to refer to the twelve people. – 2017-02-09
2 Answers
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There's only one president, and it's equally likely to be any of the 12 people, so 1/12.
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Since the committee is consisten from 6 memberand there are 12 people to choose from, the propability of Erik to be choosen in the committee is 1/2. Since there are 3 title for members, the propability of Erik getting a title is 1/2, given that Erik is choosen in the committee. Since 1 out of 3 titles is the president, there is 1/3 propability of Erik getting to be the president, given that Erik is choosen to get a title.
Hence the propability of Erik getting the president title is 1/2*1/2*1/3=1/12.