Last visit was: 04 Nov 2024, 20:21 It is currently 04 Nov 2024, 20:21

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36111 [3]
Given Kudos: 25918
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36111 [0]
Given Kudos: 25918
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [0]
Given Kudos: 136
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [0]
Given Kudos: 136
Send PM
Re: A gardener is going to plant 2 red rosebushes and 2 white ro [#permalink]
Carcass 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 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 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
Manager
Manager
Joined: 19 Jun 2021
Posts: 52
Own Kudos [?]: 27 [0]
Given Kudos: 24
Send PM
Re: A gardener is going to plant 2 red rosebushes and 2 white ro [#permalink]
We have 4 plants, so we can arrange them in 4! ways = 24 ways

Hey, why is it 4! line all plants are different?
You have 2 white and 2 red. I assumed that you cannot distinguish between them and I counted the total amount as:
(4!)/(2!2!)

Why did you count it as you have 4 different plants?


GreenlightTestPrep wrote:
Carcass 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 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

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,
Verbal Expert
Joined: 18 Apr 2015
Posts: 29887
Own Kudos [?]: 36111 [1]
Given Kudos: 25918
Send PM
Re: A gardener is going to plant 2 red rosebushes and 2 white ro [#permalink]
1
Expert Reply
We are asked to find the probability of one particular pattern: WRRW.

Total # of ways a gardener can plant these four bushes is the # of permutations of 4 letters WWRR, out of which 2 W's and 2 R's are identical, so \(\frac{4!}{2!2!}=6\);

So \(p=\frac{1}{6}\).

Answer: B.


Or you can do with direct probability approach:

The probability that the first rosebush will be white is 2/4 (there are two white out of total 4 rosebushes);
The probability that the second rosebush will be red is 2/3 (there are two reds out of total 3 rosebushes left);
The probability that the third rosebush will be red is 1/2 (there are now one red out of total 2 rosebushes left);
Finally, only one white is left so the probability is 1;

P(WRRW)=2/4*2/3*1/2*1=1/6.

Answer: B.
Prep Club for GRE Bot
Re: A gardener is going to plant 2 red rosebushes and 2 white ro [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
228 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne