Probability - HELP - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Probability - HELP

Expert replies

soni_pallavi: Master | Next Rank: 500 Posts; Posts: 107; Joined: Tue Jun 05, 2012 3:25 amFollowed by: 13 members; Thanked: 1 times

by soni_pallavi » Mon Oct 29, 2012 2:51 am

Hi

Could anyone show the working of this question.

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 two rose bushes in the middle will be red??

Thanks

Like this post

Source: Beat The GMAT — Problem Solving | Mon Oct 29, 2012 2:51 am

GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Oct 29, 2012 4:00 am

soni_pallavi wrote:Hi

Could anyone show the working of this question.

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 two rose bushes in the middle will be red??

Thanks

Probability that the first rosebush will be white = 2/4
Now there are 2 reds out of total 3 rosebushes left, so probability that the second rosebush will be red = 2/3
Now one red rosebush out of total 2 rosebushes is left, so probability that the third rosebush will be red = 1/2
Now, one white rosebush is left so the probability = 1

Probability that 2 rose bushes in the middle will be red = 2/4 * 2/3 * 1/2 * 1 = [spoiler]1/6[/spoiler]

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 29, 2012 5:13 am

soni_pallavi wrote:Hi

Could anyone show the working of this question.

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 two rose bushes in the middle will be red??

Thanks

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon May 19, 2014 7:42 am

Brent@GMATPrepNow wrote:
soni_pallavi wrote:Hi

Could anyone show the working of this question.

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 two rose bushes in the middle will be red??

Thanks
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

Cheers,
Brent

Hello Brent,

I was just wondering if the following approach is also OK:

I first select two red rose bushes for the middle i.e.

- 2/4 1/3 -

I then select the two white bushes for the sides i.e.

2/2 2/4 1/3 1/1

= 1/6

Thanks a lot for your help.

Best Regards,
Sri

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon May 19, 2014 8:24 am

That solution is perfect, Sri.
Great approach!!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Mon May 19, 2014 10:52 am

Hi Sri,

You can use your approach and work "from left to right"; you'll get the same answer:

We want W R R W

2/4 2/3 1/2 1/1

= 4/24 = 1/6

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

Contact Rich at [email protected]

Like this post

parveen110: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Fri Jan 17, 2014 7:34 am; Thanked: 7 times

by parveen110 » Mon Jun 02, 2014 2:15 am

Just would like to implement one of the important things about probablity that i learnt through many posts on this forum: It doesn't matter how you count things, as long as you're consistent.

Coming to the problem:
Let two red and two white rose bushes are identical.

So, The desired combination is: WRRW

Total outcomes= 4!/2!.2!=24/4=6

Favourable outcome= 1

Probablity of planting two red bushes in the middle= FO/TO= 1/6

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review