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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If a jury of 12 people is to be selected randomly from a ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If a jury of 12 people is to be selected randomly from a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? A. 24/91 B. 45/91 C. 2/3 D. 67/91 E. 84/91 OA D Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? A. 24/91 B. 45/91 C. 2/3 D. 67/91 E. 84/91 OA D Source: Manhattan Prep We see that 2/3 x 15 = 10 potential jurors are male and thus 5 are female. We want to have at least 2/3 x 12 = 8 men to be selected as jurors and thus at most 4 women to be selected as jurors. The number of ways to select 8 men and 4 women is 10C8 x 5C4 = 10C2 x 5C1 = (10 x 9)/2 x 5 = 45 x 5 = 225. The number of ways to select 9 men and 3 women is 10C9 x 5C3 = 10C1 x 5C2 = 10 x (5 x 4)/2 = 10 x 10 = 100. The number of ways to select 10 men and 2 women is 10C10 x 5C2 = 1 x (5 x 4)/2 = 1 x 10 = 10. The total number of ways of selecting 12 people from 15 is 15C12 = 15C3 = (15 x 14 x 13)/(3 x 2) = 5 x 7 x 13 = 455. Therefore, the probability that the jury will comprise at least 2/3 men is (225 + 100 + 10)/455 = 335/455 = 67/91. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? A. 24/91 B. 45/91 C. 2/3 D. 67/91 E. 84/91 Question rephrased: What is the probability that at least 8 men will be selected to serve on the 12-member jury? P(good outcome) = 1 - P(bad outcome). Here, a BAD outcome means selecting a jury with FEWER than 8 men. Of the 10 men and 5 women in the jury pool, 3 people must be selected NOT to serve on the jury. There is only ONE WAY to select fewer than 8 men FOR the jury: The 3 people selected NOT to serve on the jury must ALL be men, leaving 7 men and all 5 women to serve on the jury. P(1st non-juror is a man) = 10/15. (Of the 15 people in the jury pool, 10 are men.) P(2nd non-juror is a man) = 9/14. (Of the 14 remaining people in the jury pool, 9 are men.) P(3rd non-juror is a man) = 8/13. (Of the 13 remaining people in the jury pool, 8 are men.) Since a bad outcome requires that all 3 events happen, we MULTIPLY the fractions: 10/15 * 9/14 * 8/13 = 24/91. Thus: P(good outcome) = 1 - 24/91 = 67/91. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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