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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 tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ### Top Member ## There are 10 books on a shelf: 5 English books, 3 Spanish ## 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 Tutor ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12995 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Top Reply VJesus12 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 Let's use the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P( 2 different languages) = 1 - P(NOT 2 different languages) So, we can write: P(2 different languages) = 1 - P(the 2 languages are the SAME) P(the 2 languages are the SAME) P(the 2 languages are the SAME) = P(both books are English OR both books are Spanish OR both books are Portuguese ) = P(both books are English) + P(both books are Spanish) + P(both books are Portuguese ) = P(1st book is English AND 2nd book is English) + P(1st book is Spanish AND 2nd book is Spanish) + P(1st book is Portuguese AND 2nd book is Portuguese) = [P(1st book is English) x P(2nd book is English)] + [P(1st book is Spanish) x P(2nd book is Spanish)] + [P(1st book is Portuguese) x (P(2nd book is Portuguese)] = [5/10 x 4/9] + [3/10 x 2/9] + [2/10 x 1/9] = 20/90 + 6/90 + 2/90 = 28/90 = 14/45 So, P(2 different languages) = 1 - 14/45 = 31/45 Answer: D Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 VJesus12 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 Tutor 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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