Let X be a continuous uniform R.V. between $x_a$ and $x_b$ and $Y_1$ and $Y_2$ be identically distributed continuous uniform R.V. between $y_a$ and $y_b$. $y_a$ and $y_b$ and sandwiched in between $x_a$ and $x_b$. All three R.V.'s are independent. What's the probability that X is realized smaller than the two Y's?
We take the probability that X is realized from $x_a$ to $y_a$ and add it to the probability that X is realized within $y_a$ and $y_b$ AND is less than both $Y_1$ and $Y_2$. I had previously asked how one can determine that one R.V. is realized smaller than another random variable, but the question of whether it's smaller than two (or potentially even more R.V.'s) has me puzzled.