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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 ## Romeo and Juliet play a dice game in which the two tagged by: swerve ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Romeo and Juliet play a dice game in which the two ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Romeo and Juliet play a dice game in which the two participants take turns rolling a single fair six-sided die. The first player to roll 6 wins. If Rome rolls first, what is the probability that Juliet will win? A. $$\frac{1}{4}$$ B. $$\frac{1}{3}$$ C. $$\frac{4}{9}$$ D. $$\frac{5}{11}$$ E. $$\frac{1}{2}$$ The OA is D Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 swerve wrote: Romeo and Juliet play a dice game in which the two participants take turns rolling a single fair six-sided die. The first player to roll 6 wins. If Rome rolls first, what is the probability that Juliet will win? A. $$\frac{1}{4}$$ B. $$\frac{1}{3}$$ C. $$\frac{4}{9}$$ D. $$\frac{5}{11}$$ E. $$\frac{1}{2}$$ Let P(R) = the probability that Romeo wins and P(J) = the probability that Juliet wins. Since there are only two possible outcomes -- either Romeo wins or Juliet wins -- we get: P(R) + P(J) = 1 Probability that Romeo wins on the first roll = 1/6 Probability that Romeo wins on the third roll = 1/6 + (5/6)(5/6)(1/6) Probability that Romeo wins on the fifth roll = 1/6 + (5/6)(5/6)(1/6) + (5/6)(5/6)(5/6)(5/6)(1/6) And so on. Thus: P(R) = 1/6 + (5/6)(5/6)(1/6) + (5/6)(5/6)(5/6)(5/6)(1/6)... Probability that Juliet wins on the second roll = (5/6)(1/6) Probability that Juliet wins on the fourth roll = (5/6)(1/6) + (5/6)(5/6)(5/6)(1/6) Probability that Juliet wins on the sixth roll = (5/6)(1/6) + (5/6)(5/6)(5/6)(1/6) + (5/6)(5/6)(5/6)(5/6)(5/6)(1/6) And so on. Thus: P(J) = (5/6)(1/6) + (5/6)(5/6)(5/6)(1/6) + (5/6)(5/6)(5/6)(5/6)(5/6)(1/6)... The blue portions common to P(R) and P(J) indicate the following: P(J) = (5/6)P(R) P(R) = (6/5)P(J) Substituting P(R) = (6/5)P(J) into P(R) + P(J) = 1, we get: (6/5)P(J) + P(J) = 1 (11/5)P(J) = 1 P(J) = 5/11 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. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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