medium Probability
A release-checked medium problem for training Law of Total Probability, Uniform, Geometric Probability, Order Statistics.
Lewis is cutting a piece of wood of length $L$ into three pieces. In order to cut the wood, he independently and uniformly at random chooses two cutpoints, one on each side of the midpoint of the piece of wood. What is the probability that the distance between Lewis' two cutpoints is less than $\frac{L}{3}$? Record the answer when $L = 2$.
This Probability problem is tagged Law of Total Probability, Uniform, Geometric Probability, Order Statistics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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