Break the Stick
Probability
Level
2
A stick is broken into 2 at a point selected uniformly at random. What is the probability that the longer piece is at least times as long as the shorter piece?
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1 solution
WLOG, lets assume that the stick has unit length.
If the longer piece is at least x times longer than the shorter piece, this implies that the cut was made within x + 1 1 of either side, assuming x > 1 , which is a reasonable assumption here.
Therefore, since this can be on either side the probability will be double this, or:
P = x + 1 2