My professor did this problem out of our text book and he didn't exactly show us how he did it (he skipped showing the steps in the middle). He got the answer $(1-x)^2$.
If we let $X$ and $Y$ be two independent uniform $(0,1)$ random variables and let $M$ be the minimum of $X$ and $Y$, $0\lt x \lt 1$. How would we represent the event $(M\ge x)$ as the region in the plane and find $P(M\ge x)$ in the area of this region?
How would you go about doing this?
PS I added the homework tag because it could have been a homework problem, however it's not homework. I'm just looking for more people to see my question.