Suppose that A, B, C, are independent random variables, each being uniformly distributed over (0, 1).

(a) What is the joint cumulative distribution function of A, B, C?

(b) What is the probability that all of the roots of the equation Ax2 + Bx + C = 0 are real?

For (a) it's pretty clear that this defines a cube in $\displaystyle \mathbb{R}_3$. $\displaystyle F_{a,b,c}(a,b,c)=a*b*c$

For part (b) the discriminate has to be greater then zero so I need to find $\displaystyle P(B^2-4AC>0)=P(B^2>4AC)$

I'm not entirely sure how to go about finding this. I know I need to convert this into some expression of volume but I'm not sure how.