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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 ## Events A and B are independent and have equal probabilities ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Events A and B are independent and have equal probabilities ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? (1) The probability that at least one of events A and B occurs is 0.84. (2) The probability that event B occurs and event A does not is 0.24. OA A Source: Veritas Prep ### 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: Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs? (1) The probability that at least one of events A and B occurs is 0.84. (2) The probability that event B occurs and event A does not is 0.24. Statement 1: P(at least one event occurs) = 1 - P(neither event occurs) Thus: P(at least A or B) = 1 - P(neither A nor B) Since P(at least A or B) = 0.84, we get: 0.84 = 1 - P(neither A nor B) P(neither A nor B) = 0.16 P(not A) * P(not B) = 0.16. Since it is given that P(A) = P(B), P(not A) = P(not B). Substituting P(not A) = P(not B) into P(not A) * P(not B) = 0.16, we get: [P(not A)]Â² = 0.16 P(not A) = 0.4 P(A) = 1 - 0.4 = 0.6 SUFFICIENT. Statement 2: Try to recycle the result yielded by Statement 1: P(A) = P(B) = 0.6 Case 1: P(B) = P(A) = 0.6 and P(not A) = 0.4, with the result that P(B but not A) = (0.6)(0.4) = 0.24 The values in blue can be reversed, as follows: Case 2: P(B) = P(A) = 0.4 and P(not A) = 0.6, with the result that P(B but not A) = (0.4)(0.6) = 0.24 Since P(A) can be different values, INSUFFICIENT. The correct answer is A. _________________ 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 • Award-winning private GMAT tutoring Register now and save up to$200

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