A stick is cut into 3 in a uniformly random manner. What is the probability that all three will form a triangle?

Probability Puzzles: Cutting a Stick to form a Triangle

Printable View

- Dec 18th 2012, 10:46 AMbroccoli7Triangle Formation Probability
A stick is cut into 3 in a uniformly random manner. What is the probability that all three will form a triangle?

Probability Puzzles: Cutting a Stick to form a Triangle - Dec 18th 2012, 11:07 AMebainesRe: Triangle Formation Probability
The pieces can't make a triangle if any one of the three piece is greater than half the length of the stick. Imagine a stick 1 meter in length, and the locations of the two cuts are measured from the left end of the stick. Call the two points of the cuts A and B. The pieces will not be able to form a triangle if (A> 0.5 and B> 0.5) or (A< 0.5 and B<0.5) or (A<0.5 and B> A+0.5) or (A > 0.5 and B< A-0.5). You can add these up to get the probability that the pieces won't make a triangle is 0.75. Hence the probability that they do make a triangle is

**0.25**. - Dec 25th 2012, 09:57 AMbroccoli7Re: Triangle Formation Probability
Yes, thanks for the input. That is also a nice different way to look at the puzzle.