A gardener is going to plant 2 red rosebushes and 2 white rosebushes.

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pm; Followed by:1 members

A gardener is going to plant 2 red rosebushes and 2 white rosebushes.

by BTGModeratorVI » Thu Jul 23, 2020 6:42 am

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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

Answer: B
Source: GMAT Paper Tests

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Source: Beat The GMAT — Problem Solving | Thu Jul 23, 2020 6:42 am

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

Re: A gardener is going to plant 2 red rosebushes and 2 white rosebushes.

by Brent@GMATPrepNow » Sat Jul 25, 2020 6:39 am

BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:42 am
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

Answer: B
Source: GMAT Paper Tests

Let's 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

Answer: B

Cheers,

Brent Hanneson - Creator of GMATPrepNow.com

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gentvenus: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue Oct 01, 2019 5:49 am

Re: A gardener is going to plant 2 red rosebushes and 2 white rosebushes.

by gentvenus » Sat Jul 25, 2020 11:10 am

P = 4/4! = 1/6

B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: A gardener is going to plant 2 red rosebushes and 2 white rosebushes.

by Scott@TargetTestPrep » Sun Jul 26, 2020 8:50 am

BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:42 am
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

Answer: B
Source: GMAT Paper Tests

Solution:

We need to determine the probability of white-red-red-white.

Let’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

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