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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 ## a family has 5 children, what is the probability that there tagged by: GMATinsight ##### This topic has 3 expert replies and 0 member replies ## a family has 5 children, what is the probability that there ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult a family has 5 children, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 Source: www.GMATinsight.com Answer: Option E _________________ Bhoopendra Singh & Sushma Jha - Founder "GMATinsight" Testimonials e-mail: info@GMATinsight.com I Mobile: +91-9999687183 / +91-9891333772 To register for One-on-One FREE ONLINE DEMO Class Call/e-mail One-On-One Private tutoring fee - US$40 per hour & for FULL COURSE (38 LIVE Sessions)-US$1000 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15093 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 The problem should make clear that P(boy) = P(girl) = 1/2: Quote: A family has 5 children. If each child is equally likely to be a boy or a girl, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 P(exactly n times) = P(one way) * total possible ways. Let B = boy and G = girl. P(one way): One way to get exactly 3 boys and 2 girls is BBBGG. P(BBBGG) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32. Total possible ways: Any arrangement of the letters BBBGG will yield exactly 3 boys and 2 girls. Thus, to account for all the ways to get exactly 3 boys and 2 girls, the result above needs to be multiplied by the number of ways to arrange BBBGG. Number of ways to arrange BBBGG = 5!/(3!2!) = 10. Multiplying the results above, we get: P(exactly 3 boys and 2 girls) = 10 * 1/32 = 10/32 = 5/16. The correct answer is E. _________________ 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: 1273 messages Followed by: 29 members Upvotes: 59 Quote: A family has 5 children. If each child is equally likely to be a boy or a girl, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 Source: www.GMATinsight.com $? = P\left( {3B\,\,{\text{and}}\,\,2G\,\,{\text{among}}\,\,5\,\,{\text{children}}} \right)$ Imagine 3 B´s and 2 G´s in a row... each sequence is associated with the children´s sexuality, from (say) the older to the younger child. Total number: 2^5 = 32 equiprobable sequences (for instance starting with BBBBB and ending with GGGGG.) Favorable number: C(5, 3) = 10 , because we must choose among the 5 positions in the sequence, 3 of them to "put" the B´s (and the remaining 2 to "put" the G´s). $? = \frac{{C\left( {5,3} \right)}}{{32}} = \frac{{10}}{{32}} = \frac{5}{{16}}$ This solution follows the notations and rationale taught in the GMATH method. Regards, fskilnik. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Last edited by fskilnik@GMATH on Wed Sep 26, 2018 2:18 pm; edited 1 time in total ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2006 messages Followed by: 14 members Upvotes: 43 GMATinsight wrote: a family has 5 children, what is the probability that there are 3 boys and 2 girls among the children? A) 1/32 B) 1/16 C) 3/32 D) 1/4 E) 5/16 The number of 5 children of any sex is 2 x 2 x 2 x 2 x 2 = 2^5 = 32. The number of ways that the 5 children could be 3 boys and 2 girls is 5!/(3! x 2!) = (5 x 4)/2! = 10. Therefore, the probability is 10/32 = 5/16. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 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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