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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 fair 6-sided die is rolled three times, what is the tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If a fair 6-sided die is rolled three times, what is the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Veritas Prep If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled? A. $$\frac{25}{216}$$ B. $$\frac{50}{216}$$ C. $$\frac{25}{72}$$ D. $$\frac{25}{36}$$ E. $$\frac{5}{6}$$ OA C ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15385 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: Veritas Prep If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled? A. $$\frac{25}{216}$$ B. $$\frac{50}{216}$$ C. $$\frac{25}{72}$$ D. $$\frac{25}{36}$$ E. $$\frac{5}{6}$$ P(exactly n times) = P(one way) * all possible ways. Let T = 3 and N = not 3. P(one way): One way to get exactly one 3: TNN. P(T on the 1st roll) = 1/6. (Of the 6 possible rolls, one is 3.) P(N on the 2nd roll) = 5/6. (Of the 6 possible rolls, five are not 3.) P(N on the 3nd roll) = 5/6. (Of the 6 possible rolls, five are not 3.) Since we want all of these events to happen, we MULTIPLY: 1/6 * 5/6 * 5/6 = 25/216. All possible ways: TNN is only ONE WAY to exactly one 3. Now we must account for ALL OF THE WAYS to get exactly one 3. Any arrangement of the letters TNN represents one way to exactly one 3. Thus, to account for ALL OF THE WAYS to get exactly one 3, the result above must be multiplied by the number of ways to arrange the letters TNN. Number of ways to arrange 3 elements = 3!. But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED. The reason: When the identical elements swap positions, the arrangement doesn't change. Here, we must divide by 2! to account for the two identical N's: 3!/2! = 3. Multiplying the results above, we get: P(exactly one 3) = 25/216 * 3 = 25/72. The correct answer is C. More practice: https://www.beatthegmat.com/select-exactly-2-women-t88786.html https://www.beatthegmat.com/probability-gmat-prep-t114250.html https://www.beatthegmat.com/a-single-particle-is-accelerated-through-a-magnetic-field-wh-t228342.html https://www.beatthegmat.com/at-a-blind-taste-competition-a-contestant-is-offered-3-cups-t220058.html https://www.beatthegmat.com/rain-check-t79099.html https://www.beatthegmat.com/probability-t227448.html _________________ 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 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 AAPL wrote: Veritas Prep If a fair 6-sided die is rolled three times, what is the probability that exactly one 3 is rolled? A. $$\frac{25}{216}$$ B. $$\frac{50}{216}$$ C. $$\frac{25}{72}$$ D. $$\frac{25}{36}$$ E. $$\frac{5}{6}$$ OA C We can let Y = rolling a 3 and N = not rolling a 3. So we need the probability of Y-N-N: P(Y-N-N) = 1/6 x 5/6 x 5/6 = 25/216 Since Y- N-N can take place in 3!/2! = 3 ways, the total probability is 3 x 25/216 = 75/216 = 25/72. Answer: C _________________ 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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