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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 magician has five animals in his magic hat: 3 doves and 2 tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A magician has five animals in his magic hat: 3 doves and 2 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMAT Prep A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair? A. 2/5 B. 3/5 C. 1/5 D. 1/2 E. 7/5 OA A ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: GMAT Prep A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair? A. 2/5 B. 3/5 C. 1/5 D. 1/2 E. 7/5 AND means MULTIPLY. OR means ADD. Case 1: 2 doves P(1st animal is a dove) = 3/5. (Of the 5 animals, 3 are doves.) P(2nd animal is a dove) = 2/4. (Of the 4 remaining animals, 2 are doves.) Since in Case 1 we need the 1st animal to be a dove AND the 2nd animal to be a dove, we MULTIPLY the fractions: 3/5 * 2/4 = 6/20 = 3/10 Case 2: 2 rabbits P(1st animal is a rabbit) = 2/5. (Of the 5 animals, 2 are rabbits.) P(2nd animal is a rabbit) = 1/4. (Of the 4 remaining animals, 1 is a rabbit.) Since in Case 2 we need the 1st animal to be a rabbit AND the 2nd animal to be a rabbit, we MULTIPLY the fractions: 2/5 * 1/4 = 2/20 = 1/10 Since a good outcome will be yielded by Case 1 OR by Case 2, we ADD the blue fractions: 3/10 + 1/10 = 4/10 = 2/5 The correct answer is A. _________________ 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 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: GMAT Prep A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair? A. 2/5 B. 3/5 C. 1/5 D. 1/2 E. 7/5 OA A Let's apply probability rules First notice that, to get a matched pair, we can select 2 doves or 2 rabbits. So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove) We can now apply our AND and OR rules to get: P(matched pair) = [P(1st pick is rabbit) x P(2nd pick is rabbit)] + [P(1st pick is dove) x P(2nd pick is dove)] So, P(matched pair) = (3/5 x 2/4) + (2/5 x 1/4) We get: 2/5 (or 0.4) Answer: A 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: 2791 messages Followed by: 18 members Upvotes: 43 AAPL wrote: GMAT Prep A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance that he will have a matched pair? A. 2/5 B. 3/5 C. 1/5 D. 1/2 E. 7/5 OA A We are given that from a group of 3 doves and 2 rabbits, 2 animals will be randomly selected. We need to determine the probability that a matched pair will be pulled out of the hat. In other words, we need to determine: P(2 doves pulled) + P(2 rabbits pulled) We can use combinations to determine the number of favorable outcomes (that 2 rabbits or 2 doves are selected) and the total number of outcomes (that 2 animals are selected from 5). Letâ€™s first determine the number of ways we can select 2 doves from 3: # of ways to select 2 doves from 3 doves: 3C2 = 3 Next letâ€™s determine the number of ways we can select 2 rabbits from 2: # of ways to select 2 rabbits from 2 rabbits: 2C2 = 1 Now we must determine the number of ways to select 2 animals from a total of 5 animals: 5C2 = (5 x 4)/(2 x 1) = 10 Thus, the probability of selecting a matched pair is 3/10 + 1/10 = 4/10 = 2/5. Alternate Solution: The two events that satisfy the requirement of getting a matched pair are DD or RR. The probability of DD is 3/5 x 2/4 = 6/20 =3/10. The probability of RR is 2/5 x 1/4 = 2/20 = 1/10. Since DD and RR are mutually exclusive events, the probability that either of these two events happens can be found simply by adding the individual probabilities, which is 3/10 + 1/10 = 4/10 = 2/5. Answer: A _________________ 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 GMAT Exam Know how you'd score today for$0

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