The random variables $X$, $Y$, $Z$ are independent and uniformly distributed in $[0,1]$. What is the probability of real roots of $Xt^2+Yt+Z=0$?
So the equation has a real root when $Y^2\geq 4XZ$. Given that the variables are independent, the joint density is $f(x,y,z) = 1$ in the unit cube $[0,1]^3$, and $0$ otherwise. My guess is that I need to integrate the volume between the surface $y^2=4xz$ and $y=0$ inside the unit cube. My calculus is rusty so I need help on how to proceed.