Let there be two identical and independent random variables $X$ and $Y$. Both $X$ and $Y$ are uniformly distributed from $0$ to $50$. What is the probability that $|X - Y| < 10$? This is not homework. I am practicing probability.
I think if $|X - Y| < 10$, then either $X$ is greater than $Y$ or $Y$ is greater than $X$, the expected value of $A = |X - Y|$ should be $\int_0^{50} \int_0^y (y - x) \, dx \, dy + \int_0^{50} \int_0^x (x - y) \, dy \, dx = \frac{125000}{3}$, but how to do I use this value to find $P(A < 10)$?