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If a point is arbitrarily selected on a line segment, thus breaking it into two smaller segments, what is the probabilit

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If a point is arbitrarily selected on a line segment, thus breaking it into two smaller segments, what is the probabilit

by Gmat_mission » Sun Aug 08, 2021 10:14 am

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If a point is arbitrarily selected on a line segment, thus breaking it into two smaller segments, what is the probability that the larger segment is at least twice as long as the smaller one?

A. \(\dfrac14\)

B. \(\dfrac13\)

C. \(\dfrac12\)

D. \(\dfrac23\)

E. \(\dfrac34\)

Answer: D

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Re: If a point is arbitrarily selected on a line segment, thus breaking it into two smaller segments, what is the probab

by regor60 » Wed Aug 11, 2021 9:57 am
For the larger segment to be at least twice as long as the shorter it has to be at least 2/3 of the overall length, with the shorter segment being then <1/3 of the length.

So, a cut could be placed anywhere in the 1/3 of the segment to the left of the right end. The probability of this is then 1/3.

But the cut could also be placed in the 1/3 of the line to the right of the left end, which also has probability of 1/3.

So the total probability is [spoiler]2/3,D[/spoiler]
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