easy Probability
A release-checked easy problem for training Uniform, Geometric Probability.
A right triangle is being formed with leg lengths $X$ and $Y$, where $X,Y \sim \unif{0}{1}$ IID. Let $\theta$ be the measure of the (random) angle that is opposite of side $Y$. Find $\prob{\theta > \dfrac{\pi}{3}}$. If necessary, round to the nearest thousandth.
This Probability problem is tagged Uniform, Geometric Probability. 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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