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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 Eight women and two men are available to serve on a tagged by: BTGmoderatorLU This topic has 4 expert replies and 1 member reply Top Member Eight women and two men are available to serve on a Timer 00:00 Your Answer A B C D E Global Stats Difficult Source: Manhattan GMAT Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man? A. 1/32 B. 1/4 C. 2/5 D. 7/15 E. 8/15 The OA is E GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: Manhattan GMAT Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man? A. 1/32 B. 1/4 C. 2/5 D. 7/15 E. 8/15 P(at least 1 man) = 1 - P(no men). P(no men): P(1st person selected is a woman) = 8/10. (Of the 10 people, 8 are women.) P(2nd person selected is a woman) = 7/9. (Of the 9 remaining people, 7 are women.) P(3rd person selected is a woman) = 6/8. (Of the 8 remaining people, 6 are women.) To combine these probabilities, we multiply: 8/10 * 7/9 * 6/8 = 7/15. Thus: P(at least 1 man) = 1 - 7/15 = 8/15. The corrected answer is E. _________________ 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. GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Manhattan GMAT Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man? A. 1/32 B. 1/4 C. 2/5 D. 7/15 E. 8/15 $\left\{ \begin{gathered} \,8\,\,{\text{women}} \hfill \\ \,2\,\,{\text{men}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,P\left( {\, \geqslant 1\,\,{\text{men}}\,\,{\text{in}}\,\,3\,\,{\text{people}}\,} \right)$ $?\,\,\, = \,\,\,1 - P\left( {3\,\,{\text{women}}\,\,{\text{in}}\,\,3\,\,{\text{people}}} \right)\,\,\, = \,\,\,1 - \frac{{C\left( {8,3} \right)}}{{\,C\left( {10,3} \right)\,}}\,\,\, = \,\,\,1 - \frac{7}{{15}}\,\,\, = \,\,\,\frac{8}{{15}}$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man? A. 1/32 B. 1/4 C. 2/5 D. 7/15 E. 8/15 When it comes to probability questions involving "at least," it's best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting at least 1 man) = 1 - P(not getting at least 1 man) What does it mean to not get at least 1 man? It means getting ZERO men. So, we can write: P(getting at least 1 man) = 1 - P(getting ZERO men) P(getting ZERO men) P(getting ZERO men) = P(all 3 selections are women) = P(1st selection is a woman AND 2nd selection is a woman AND 3rd selection is a woman) = P(1st selection is a woman) x P(2nd selection is a woman) x P(3rd selection is a woman) = 8/10 x 7/9 x 6/8 = 7/15 So we get: P(getting at least 1 man) = 1 - 7/15 = 8/15 Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Top Member Legendary Member Joined 02 Mar 2018 Posted: 1121 messages Followed by: 2 members There are 8 women and 2 men What is the probability of picking at least one man if 3 people are picked Total = 8 + 2 Probability that the committee doesn't include a man. $$\frac{8}{10}\cdot\frac{7}{9}\cdot\frac{6}{8}=\frac{336}{720}=\frac{7}{15}$$ Probability that the committee includes at least one man = 1 - p $$=\ 1-probability\ \ of\ committee\ not\ pick\ any\ man$$ $$=1-\frac{7}{15}=\frac{8}{15}$$ $$answer\ is\ Option\ E$$ GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Manhattan GMAT Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man? A. 1/32 B. 1/4 C. 2/5 D. 7/15 E. 8/15 The OA is E We can use the equation: The number of committees with at least one man = (the total number of committees) - (the number of committees without a man) The total number of committees = 10C3 = 10!/(3! x 7!) = (10 x 9 x 8)/3! = 720/6 = 120 The number of committees without a man = 8C3 x 2C0 = (8 x 7 x 6)/3! x 1 = 56 Therefore, the number of committees with at least one man = 120 - 56 = 64 and the probability of selecting such a committee is 64/120 = 8/15. Answer: E _________________ 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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