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A stick is broken at two points, chosen at random. If the length of the stick is  then what is the probability that all three resulting pieces are shorter than  units?

 

Any help would be much appreciated!

 May 7, 2023
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The probability that all three pieces are shorter than 5 units is equal to the probability that the first break is less than 5 units and the second break is less than 5 units.

The probability that the first break is less than 5 units is 5/6​.

The probability that the second break is less than 5 units is 5/6.

The probability that both breaks are less than 5 units is 5/6*5/6​=25/36​​.

 May 7, 2023

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