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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 ## There are 10 books on a shelf: 5 English books, 3 Spanish bo ##### This topic has 3 expert replies and 0 member replies ### Top Member ## There are 10 books on a shelf: 5 English books, 3 Spanish bo ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult There are 10 books on a shelf: 5 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages? A. 31/90 B. 3/10 C. 1/3 D. 31/45 E. 28/90 OA D Source: Economist Gmat ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: There are 10 books on a shelf: 5 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages? A. 31/90 B. 3/10 C. 1/3 D. 31/45 E. 28/90 OA D Source: Economist Gmat We can use the formula: P(choosing two books of different language) = 1 - P(choosing two books of same language) So our options are 2 English, 2 Spanish or 2 Portuguese books. 2 English books can be chosen in: 5C2 = (5 x 4)/2! = 10 ways 2 Spanish books can be chose in: 3C2 = 3 ways 2 Portuguese books can be chosen in: 2C2 = 1 way The total ways to select 2 books from 10 is: 10C2 = (10 x 9)/2 = 45 ways So P(choosing two books of same language) = (3 + 10 + 1)/45 = 14/45. Thus, P(choosing two books of different language) = 1 - 14/45 = 31/45. Alternate Solution: If the first book is an English book (for which there is a 5/10 = 1/2 probability), the second book can be any of the 3 + 2 = 5 books among the 9 remaining books. Therefore, the probability of choosing an English book followed by a book in a different language is 1/2 x 5/9 = 5/18. If the first book is a Spanish book (for which there is a 3/10 probability), the second book can be any of the 5 + 2 = 7 books among the 9 remaining books. Therefore, the probability of choosing an Spanish book followed by a book in a different language is 3/10 x 7/9 = 21/90 = 7/30. If the first book is a Portuguese book (for which there is a 2/10 = 1/5 probability), the second book can be any of the 5 + 3 = 8 books among the 9 remaining books. Therefore, the probability of choosing an Portuguese book followed by a book in a different language is 1/5 x 8/9 = 8/45. Therefore, the total probability of choosing two books in different languages is 5/18 + 7/30 + 8/45 = 25/90 + 21/90 + 16/90 = 62/90 = 31/45. Answer: D _________________ 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: There are 10 books on a shelf: 5 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages? A. 31/90 B. 3/10 C. 1/3 D. 31/45 E. 28/90 P(2 different languages) = 1 - P(2 of the same language). Case 1: P(2 English books are selected) P(1st book is English) = 5/10. (Of the 10 books, 5 are English.) P(2nd book is English) = 4/9. (Of the 9 remaining books, 4 are English.) To combine these probabilities, we multiply: 5/10 * 4/9 = 20/90. Case 2: P(2 Spanish books are selected) P(1st book is Spanish) = 3/10. (Of the 10 books, 3 are Spanish.) P(2nd book is Spanish) = 2/9. (Of the 9 remaining books, 2 are Spanish.) To combine these probabilities, we multiply: 3/10 * 2/9 = 6/90. Case 3: P(2 Portuguese books are selected) P(1st book is Portuguese) = 2/10. (Of the 10 books, 2 are Portuguese.) P(2nd book is Portuguese) = 1/9. (Of the 9 remaining books, 1 is Portuguese.) To combine these probabilities, we multiply: 2/10 * 1/9 = 2/90. P(2 of the same language) = Case 1 + Case 2 + Case 3 = 20/90 + 6/90 + 2/90 = 28/90 = 14/45. P(2 different languages) = 1 - 14/45 = 31/45. 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. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorDC wrote: There are 10 books on a shelf: 5 English books, 3 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages? A. 31/90 B. 3/10 C. 1/3 D. 31/45 E. 28/90 Source: Economist Gmat $$10\,\,{\rm{books}}\,\,{\rm{in}}\,\,3\,\,{\rm{langs}}\,\,\,\left\{ \matrix{ 5\,\,{\rm{engl}} \hfill \cr {\rm{3}}\,\,{\rm{span}} \hfill \cr 2\,\,{\rm{port}} \hfill \cr} \right.$$ $$? = P\left( {{\rm{2}}\,{\rm{langs}}\,\,{\rm{in}}\,\,{\rm{2}}\,\,{\rm{extractions}}} \right)$$ $${\rm{total}} = C\left( {10,2} \right) = {{10 \cdot 9} \over 2} = 45\,\,\,{\rm{equiprobables}}$$ $${\rm{favorable}}\,\, = \,\,\underbrace {5 \cdot 3}_{{\rm{engl}}\,\,\& \,\,{\rm{span}}} + \underbrace {5 \cdot 2}_{{\rm{engl}}\,\,\& \,\,{\rm{port}}} + \underbrace {3 \cdot 2}_{{\rm{span}}\,\,\& \,\,{\rm{port}}} = 31$$ $$? = {{31} \over {45}}$$ 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 • FREE GMAT Exam Know how you'd score today for$0

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