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
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
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.