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Please help me with this one.

Two points (B and C) are selected randomly on a line of length L. Find the probability that the segment BC has a length less than L / 4. It is assumed that the probability of a point falling on the segment is proportional to the length and does not depend on its location on the numerical axis OX.

nonuser
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Valentina -
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  • It is a cute problem. What have you tried so far? Maybe you have learned about various probability models before? – 311411 Apr 29 '21 at 21:31
  • It's a variant of this sort of problem (https://math.stackexchange.com/questions/1952054/probability-of-two-people-meeting-within-60-mins-with-maximum-waiting-time-is-20), for which there are many other postings. –  Apr 29 '21 at 22:35

1 Answers1

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Wlog we can assume $L=1$ and $x,y$ are coordinates of $B$ and $C$ then $\Omega$ is $[0,1]^2$ and the event is set all of $(x,y)$ such that $|x-y|\leq {1\over 4}$. Drawing this set of points in the coordinate system you can see it has area $$1-\Big({3\over 4}\Big)^2= {7\over 16}$$ which is also the answer to your question.

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nonuser
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