Let's say that we have a stick of length L and we break it up into 3 pieces randomly. Here random means that we sample two numbers a,b from the uniform continuous distribution on [0, L] such that 0 < a < b < L (If a turns out to be bigger than b, we can always rename them). So now we have three pieces, [0, a), [a, b] and [b, L]. What is the probability that these three broken pieces form a triangle?
Let's say that we have a stick of length L and we break it up into 3 pieces randomly. Here random means that we sample two numbers a,b from the uniform continuous distribution on [0, L] such that 0 < a < b < L (If a turns out to be bigger than b, we can always rename them). So now we have three pieces, [0, a), [a, b] and [b, L]. What is the probability that these three broken pieces form a triangle?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Let's say that we have a stick of length L and we break it up into 3 pieces randomly. Here random
means that we sample two numbers a,b from the uniform continuous distribution on [0, L] such that
0 < a < b < L (If a turns out to be bigger than b, we can always rename them). So now we have three
pieces, [0, a], [a, b] and [b, L]. What is the probability that these three broken pieces form a triangle?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7541876-6b62-4311-9e40-68de284681cf%2F7222faac-111f-46ee-a41d-dc2102785e03%2F22kbvm_processed.png&w=3840&q=75)
Transcribed Image Text:Let's say that we have a stick of length L and we break it up into 3 pieces randomly. Here random
means that we sample two numbers a,b from the uniform continuous distribution on [0, L] such that
0 < a < b < L (If a turns out to be bigger than b, we can always rename them). So now we have three
pieces, [0, a], [a, b] and [b, L]. What is the probability that these three broken pieces form a triangle?
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