probability

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arorag: Master | Next Rank: 500 Posts; Posts: 343; Joined: Mon Jan 21, 2008 3:28 pm; Thanked: 4 times

by arorag » Mon Sep 01, 2008 11:19 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?

ans 1/6 or 1/3????

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

Re: probability

by sudhir3127 » Mon Sep 01, 2008 11:31 am

arorag 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?

ans 1/6 or 1/3????

Probability that the first bush is W is 1/2.
Probability that the second is R is 2/3.
Probability that the third is R is 1/2.
Probability that the fourth is W is 1.

(1/2)*(2/3)*(1/2)*(1) = 1/6

other way can be

total arrangements = 4!
1 red rose cn arrange itself in 2! ways = 2
2 red rose = 2! =2

thus probability is

2*2/24 = 1/6

hope that helps

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parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

by parallel_chase » Mon Sep 01, 2008 11:40 am

all the roses can be arranged in 4! ways

two roses in the middle can be arranged in

W1R1R2W2
W2R1R2W1
W1R2R1W2
W2R2R1W1

total 4 ways.

probability = 4/4! = 1/6

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