Mathematics Asked by Ssendkrad Saizer on January 6, 2021
The question is the following:
We break a stick at a uniformly chosen random location. Find the probability that the shorter piece is less than $dfrac15$-th of the original.
My attempt: $$Pleft(X < dfrac15right) = 1 – Pleft(X ge dfrac15right) = 1 – left(1 – dfrac15right) = dfrac15$$
So my answer is that the probability is $dfrac15$.
However, I checked my answer to see if I was right, and I instead found that the answer is $dfrac25$.
Where did I go wrong?
There are two places the second cut can be made such that the smaller one is less than 1/5 the larger one. This explains why the answer is twice what you came up with.
Correct answer by MONODA43 on January 6, 2021
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