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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 gardener is going to plant 2 red rosebushes and 2 white tagged by: BTGmoderatorLU ##### This topic has 6 expert replies and 0 member replies ### Top Member ## A gardener is going to plant 2 red rosebushes and 2 white ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 The OA is B. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15256 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 Moving LEFT TO RIGHT along the row: P(1st rosebush is white) = 2/4. (Of the 4 rosebushes, 2 are white.) P(2nd rosebush is red) = 2/3. (Of the 3 remaining rosebushes, 2 are red.) P(3rd rosebush is red) = 1/2. (Of the 2 remaining rosebushes, 1 is red.) P(4th rosebush is white) = 1/1. (The one remaining rosebush is white.) Since all of these events must happen in order for the 2 middle rosebushes to be red, we MULTIPLY the fractions: 2/4 * 2/3 * 1/2 * 1 = 1/6. The correct answer is B. _________________ 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: 12829 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 The OA is B. As with many probability questions, we can also solve this using counting techniques. P(2 middle are red) = (# of outcomes with 2 red in middle)/(total number of outcomes) Label the 4 bushes as W1, W2, R1, R2 total number of outcomes We have 4 plants, so we can arrange them in 4! ways = 24 ways # of outcomes with 2 red in middle If we consider the possibilities here, we can LIST them very quickly: - W1, R1, R2, W2 - W1, R2, R1, W2 - W2, R1, R2, W1 - W2, R2, R1, W1 So, there are 4 outcomes with 2 red in middle P(2 middle are red) = 4/24 = 1/6 = B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 08 Dec 2008 Posted: 12829 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 The OA is B. We can also apply probability rules: P(2 middle bushes are red) = P(1st bush is white AND 2nd bush is red AND 3rd bush is red AND 4th bush is white) = P(1st bush is white) x P(2nd bush is red) x P(3rd bush is red) x P(4th bush is white) = 2/4 x 2/3 x 1/2 x 1/1 = 1/6 = B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 $\left\{ \begin{gathered} \,2\,\,{\text{red}} \hfill \\ \,2\,\,{\text{white}} \hfill \\ \end{gathered} \right.\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,P\left( {\,2\,\,{\text{red}}\,\,{\text{are}}\,\,{\text{in}}\,{\text{the}}\,\,{\text{middle}}} \right)$ ${\text{Total}}\,\, = \,\,4!\,\,\,{\text{equiprobable}}\,\,{\text{ways}}$ ${\text{Favorable}} = 2!\,\,\,\,({\text{for}}\,\,{\text{white}}\,\,1{\text{st}}\,\,{\text{and}}\,\,4{\text{th}}\,{\text{positions}})\,\,\,\,\, \cdot \,\,\,\,\,2!\,\,\,\,\,({\text{for}}\,\,{\text{red}}\,\,2{\text{nd}}\,\,{\text{and}}\,\,3{\text{rd}}\,{\text{positions}})$ $? = \frac{{\,2!\,\, \cdot 2!\,}}{{4!}} = \,\,\frac{1}{6}$ 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 ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10124 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, The math that's required to answer this question can actually be done in a couple of different ways, depending on how you "see" probability questions. We're given 2 red rosebushes (R1 and R2) and two white rosebushes (W1 and W2). We're told to put these 4 rosebushes in a row; the question asks for the probability that the "middle two" rosebushes are both red. Probability is defined asâ€¦ (# of ways that you want)/(# of ways that are possible) The # of ways that are possible = (4)(3)(2)(1) = 24 possible ways to arrange the 4 bushes. The specific ways that we want have to fit the following pattern: W-R-R-W The first bush must be white; there are 2 whites The second bush must be red; there are 2 reds The third bush must be red, but after placing the first red bush, there's just 1 red left The fourth bush must be white, but after placing the first white bush, there's just 1 white left = (2)(2)(1)(1) = 4 4 ways that fit what we want 24 ways that are possible 4/24 = 1/6 Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: GMAT Paper Tests A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushes at random, one at a time, and plant them in a row, what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes? A. 1/12 B. 1/6 C. 1/5 D. 1/3 E. 1/2 We need to determine the probability of white-red-red-white. Letâ€™s determine the probability of each selection. 1st selection: P(white rosebush) = 2/4 = 1/2 2nd selection: P(red rosebush) = 2/3 3rd selection: P(red rosebush) = 1/2 4th selection: P(white rosebush) = 1/1 = 1 Thus, P(white-red-red-white) = 1/2 x 2/3 x 1/2 x 1 = 1/6 Alternate solution: Using the indistinguishable permutations formula, we see that there are 4!/(2! x 2!) = 24/(2 x 2) = 6 ways (or arrangements) to plant these rosebushes. Having the two red rosebushes in the middle (i.e., white-red-red-white) is one of the 6 arrangements; thus, the probability is 1/6. Answer: B _________________ 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. 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