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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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

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

Source: GMAT Prep

Source: Beat The GMAT — Problem Solving | Sun Aug 08, 2021 10:14 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

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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