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probability q'n

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sandeep800
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probability q'n [#permalink] New post   02 Aug 2010, 20:38
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If points A and B are randomly selected from the circumference of a circle with diameter 4, what is the probability that the length of chord AB will be at least 2sqrt{3}?

can anyone please solve?



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Re: probability q'n [#permalink] New post   02 Aug 2010, 20:43
If this is a GMAT question, shouldn't we have answer choices? (A,B,C,D,E)

My guess is somewhere in the neighborhood of 50% chance chord length is at least \(2\sqrt{3}\)
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Re: probability q'n [#permalink] New post   03 Aug 2010, 03:26
I have no idea how to solve this qs
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Re: probability q'n [#permalink] New post   03 Aug 2010, 04:39
Let us call O, AB, R the center, the chord, and the radius of the circle, respectively.
\(AB\geq2\sqrt{3}\) and \(R=2\)

It is remarked that when \(AB\geq2\sqrt{3}\), the corresponding central angle \(AOB\geq120^{\circle}\)

Result = \(\frac{120^{\circle}}{360^{\circle}}=\frac{1}{3}\)
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Re: probability q'n [#permalink] New post   03 Aug 2010, 10:24
sandeep800 wrote:
If points A and B are randomly selected from the circumference of a circle with diameter 4, what is the probability that the length of chord AB will be at least 2sqrt{3}?

can anyone please solve?


Corresponding central angle for a dimater is 180, so let x be a corresponding central angle for a chord of 2sqrt3

So, x/180=2sqrt3/4

Estimate x
Is this approach correct?
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Re: probability q'n [#permalink] New post   04 Aug 2010, 22:50
I think we can use Integral (Area under the curve) for this problem. Surely, not within scope of GMAT.
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Re: probability q'n [#permalink] New post   08 Aug 2010, 19:07
bogos wrote:
Let us call O, AB, R the center, the chord, and the radius of the circle, respectively.
\(AB\geq2\sqrt{3}\) and \(R=2\)

It is remarked that when \(AB\geq2\sqrt{3}\), the corresponding central angle \(AOB\geq120^{\circle}\)

Result = \(\frac{120^{\circle}}{360^{\circle}}=\frac{1}{3}\)


How did you arrive at the 120 deg? My thinking is that the distance to a chord of length 2sqrt(3) is 1 from the center and the radius is 2, should then the probability not be 50%?



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Re: probability q'n [#permalink]
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