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# If a point is arbitrarily selected inside a circle of radius

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VP
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If a point is arbitrarily selected inside a circle of radius [#permalink]

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26 Oct 2012, 20:20
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:46) correct 30% (00:50) wrong based on 63 sessions

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If a point is arbitrarily selected inside a circle of radius R, what is the probability that the distance from this point to the center of the circle will be greater than R/2 ?

A. 1/2
B. 3/4
C. 7/8
D. 1/4*R^2
E. 3/4*R^2
[Reveal] Spoiler: OA

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Last edited by Marcab on 26 Oct 2012, 22:31, edited 1 time in total.

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Re: If a point is arbitrarily selected inside a circle of radius [#permalink]

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26 Oct 2012, 23:23
Area of circle with radius R, A1 = 2*pi*(R)^2
Area of circle with radius R/2, A2 = 2*pi*(R/2)^2

Implies, A1/A2 = 4/1

The area of the circle excluding the area of circle with radius R/2 is 3 times more..

Hence the probability will be 3/4

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Director
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Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
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Re: If a point is arbitrarily selected inside a circle of radius [#permalink]

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26 Oct 2012, 23:41
1
This post was
BOOKMARKED
Marcab wrote:
sorry....its R/2.
its been corrected in the original post.

Great now it makes sense
Basically in the question we are looking for probability of point lying in Green region in the attached figure.

Since the radius of Grean Circle is R and radius of red circle is R/2. Hence the area of greeen region =
$$pi R^2 - pi (r/2)^2$$
$$= 3/4 pi R^2$$

Also area of circle with radius R$$= pi R^2$$
Hence probability of point lying in green region =$$3/4 pi R^2 / pi R^2$$
= 3/4

Hence Ans B it is.

Hope it helps.
Attachments

circles.png [ 15.76 KiB | Viewed 1640 times ]

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Re: If a point is arbitrarily selected inside a circle of radius [#permalink]

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15 Aug 2017, 19:11
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Re: If a point is arbitrarily selected inside a circle of radius   [#permalink] 15 Aug 2017, 19:11
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