The probability that the sum of two random x y values from [0,10] is less than 13 
Two numbers $x$ and $y$ are randomly selected between $0$ to $10$. Find the probability that their sum is less than $13$.

I am scratching my head here trying to figure this out... 
Any help would be much appreciated!
 A: Implicit in "randomly selected" is "with uniform density".  This means that
the probability of $(x,y)$ lying in a (measurable) subset of the square $[0,10] \times [0,10]$ is the area of that set divided by the area of the square.

A: We assume that "randomly selected between $0$ and $10$" means that we are dealing here with two random variables $X$ and $Y$ that are independent and uniformly distributed in the interval $[0,10]$. That implies that the pair $(X,Y)$ has joint distribution that is uniform in the square with corners $(0,0)$, $(10,0)$, $(10,10)$, and $(0,10)$.
The probability that the pair $(X,Y)$ lands in a subset $A$ of the square is the area of $A$ divided by the area $100$ of the square.
In our case, the region $A$ is the part of the square that lies above the line $x+y=8$. 
To find its area, draw a picture. It is perhaps easier to find the area of the part of the square that lies below $x+y=8$. That's an isosceles right triangle with legs $8$ and therefore area $32$. Thus $A$ has area $68$.
