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If two points, A and B, are randomly placed on the circumfer

This topic has 3 expert replies and 1 member reply

If two points, A and B, are randomly placed on the circumfer

Post Thu Feb 16, 2017 11:00 am
If points A and B are randomly placed on the circumference of a circle with circumference 12pi inches, what is the probability that the length of chord AB will be at least 6 inches?

(A) 1/(2pi)
(B) 1/pi
(C) 1/3
(D) 2/pi
(E) 2/3

Source: GMAT Prep Now
Difficulty level: 700+

Answer: E

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Post Fri Feb 17, 2017 6:48 am
Hi Matt,

I checked the Mosteller link, and it seems to discuss the issues related to randomly selecting a chord, whereas my question involves choosing 2 random points that will create a chord.

The Mosteller link (in part c) seems to suggest that, if we create a chord by choosing 2 random points (as my question suggests), then the answer to my original question is 2/3

Am I missing something?

Cheers,
Brebt

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Post Fri Feb 17, 2017 1:20 am
Worth noting that randomness on a circle is a little more treacherous than you'd think. There's a good discussion in Mosteller (in the solution to problem #25) about the definition of "at random" with respect to "chords chosen at random" on a circle and how this can change the answer to a problem.

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Post Fri Feb 17, 2017 6:48 am
Hi Matt,

I checked the Mosteller link, and it seems to discuss the issues related to randomly selecting a chord, whereas my question involves choosing 2 random points that will create a chord.

The Mosteller link (in part c) seems to suggest that, if we create a chord by choosing 2 random points (as my question suggests), then the answer to my original question is 2/3

Am I missing something?

Cheers,
Brebt

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Matt@VeritasPrep GMAT Instructor
Joined
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Posted:
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625
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V51
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Post Fri Feb 17, 2017 1:20 am
Worth noting that randomness on a circle is a little more treacherous than you'd think. There's a good discussion in Mosteller (in the solution to problem #25) about the definition of "at random" with respect to "chords chosen at random" on a circle and how this can change the answer to a problem.

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  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

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