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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

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by Gmat_mission » Sun Jun 21, 2020 3:32 pm

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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

[spoiler]OA=B[/spoiler]

Source: GMAT Paper Tests
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Re: A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushe

by Brent@GMATPrepNow » Mon Jun 22, 2020 6:26 am
Gmat_mission wrote: ↑
Sun Jun 21, 2020 3:32 pm
 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

[spoiler]OA=B[/spoiler]

Source: GMAT Paper Tests
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

Answer: B

Cheers,
Brent Hanneson - Creator of GMATPrepNow.com
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Re: A gardener is going to plant 2 red rosebushes and 2 white rosebushes. If the gardener is to select each of the bushe

by Brent@GMATPrepNow » Mon Jun 22, 2020 6:26 am
Gmat_mission wrote: ↑
Sun Jun 21, 2020 3:32 pm
 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

[spoiler]OA=B[/spoiler]

Source: GMAT Paper Tests
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

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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