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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 ## In nine independent trials, what is the probability that tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 1 member reply ### Top Member ## In nine independent trials, what is the probability that ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Magoosh In nine independent trials, what is the probability that Outcome A happens at least once? 1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026. 2) The probability of Outcome A resulting in a single trial is 1/3. The OA is D ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 BTGmoderatorLU wrote: Source: Magoosh In nine independent trials, what is the probability that Outcome A happens at least once? 1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026. 2) The probability of Outcome A resulting in a single trial is 1/3. The OA is D Instead of calculating the probability that Outcome A happens at least once, it's better we calculate the probability that Outcome A does not happen even once; once we get this value, we would deduct it from 1 and get the answer. Probability that Outcome A happens at least once = 1 - Probability that Outcome A does not happen even once in 9 trials Let's take each statement one by one. 1) The probability that Outcome A does not happen even once in any of the nine trials is 0.026. => Probability that Outcome A happens at least once = 1 - Probability that Outcome A does not happen even once in 9 trials = 1 - 0.026 = A unique value. Sufficient. 2) The probability of Outcome A resulting in a single trial is 1/3. Probability that Outcome A does not happen in a single trial = 1 - 1/3 = 2/3 Probability that Outcome A does not happen even once in 9 trials = (2/3)^9 Probability that Outcome A happens at least once = 1 - (2/3)^9 = A unique value. Sufficient. The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GRE Manhattan | ACT Prep Courses San Francisco | IELTS Prep Courses Boston | Seattle IELTS Tutoring | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1104 messages Followed by: 2 members Probability of favorable outcome + probability of unfavorable outcome = 1 Probability of favorable outcome = 1 - probability of favorable outcome Probability that outcome A happens at least once = 1 - probability that outcome A never happens Statement 1 The probability that outcome A doesn't even happen even once in any of the nine trials is 0.026 Probability that outcome A happens at least once = 1 - 0.026 = 0.974 Statement 1 is SUFFICIENT. Statement 2 The probability of outcome A resulting in a single trial is 1/3 The probability that the outcome doesn't happen in a single trial. $$\frac{1}{1}-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$$ Probability that the outcome A happens in all the 9 trials $$\left(\frac{2}{3}\right)^9=\frac{2^9}{3^9}=\frac{512}{19683}=0.026$$ Probability that outcome A happens at least once = 1- 0.026 = 0.974 Statement 2 is also SUFFICIENT. Both statement alone are SUFFICIENT. $$answer\ is\ Option\ D$$ • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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