Two points are selected randomly on a line of length $30$ so as to be on opposite sides of the midpoint of the line. In other words, the two points X

and Y are independent random variables such that X is uniformly distributed over $[0,15)$ and Y is uniformly distributed over $(15,30].$ Find the probability that the distance between the two points is greater than $10.$ answerlength $30$ so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over $[0,15)$ and Y is uniformly distributed over $(15,30]$

$.$ Find the probability that the distance between the two points is greater than $10.(1$ point$)$ Two points are selected randomly on a line of length $30$ so as to be on opposite sides of the midpoint of the line. In other

words, the two points $x$ and $Y$ are independent random variables such that $x$ is uniformly distributed over $[0,15)$ and $Y$ is uniformly

distributed over $(15,30].$ Find the probability that the distance between the two points is greater than...

Explain using different methods $($Integral and Geometry$).$ Explain how you determine the integral bounds. Explain as much as possible.