[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Choose independently two numbers [math]B[/math] and [math]C[/math] at random from the

interval [math][-1,1][/math] with uniform distribution, and consider the quadratic equation

[[math]] x^2 + Bx + C = 0\ . [[/math]]

Find the probability that the roots of this equation

• are both real.
• are both positive.

Hints: (a) requires [math]0 \leq B^2 - 4C[/math], (b) requires [math]0 \leq B^2 - 4C[/math], [math]B \leq 0[/math], [math]0 \leq C[/math].