• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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... tagged by: BTGmoderatorLU ##### This topic has 5 expert replies and 1 member reply ### Top Member ## A gardener is going to plant 2 red rosebushes and 2... 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 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. I'm really confused with this PS question. Experts, any suggestion? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 LUANDATO wrote: 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 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 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 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 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 LUANDATO wrote: 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 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 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 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! Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 329 messages Upvotes: 27 Or, how many distinct permutations are there Number of permutations: 4*3*2*1 = 24 Divide by those that are the same, in this case, two red and two white 24/2!*2! = 6 distinct permutations Only one of these has two red in the middle, therefore 1/6 ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 LUANDATO wrote: 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 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. I'm really confused with this PS question. Experts, any suggestion? Thanks in advance. You could also just start by selecting bushes for the middle of the row. Probability that the first bush in the middle will be red = 2/4. Probability that second bush in the middle with also be red given that the first bush was red = 1/3. (2/4) * (1/3) = 2/12 = 1/6. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

### GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
496 members
2867
GMAT Score:
800
Hi LUANDATO,

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

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Apr 2015
Posted:
1465 messages
Followed by:
18 members
39
LUANDATO wrote:
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 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:

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.

_________________

Jeffrey Miller
jeff@targettestprep.com

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 20 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

211 posts
2 Max@Math Revolution

Math Revolution

88 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

70 posts
4 Ian Stewart

GMATiX Teacher

65 posts
5 GMATGuruNY

The Princeton Review Teacher

39 posts
See More Top Beat The GMAT Experts