[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 a number [math]B[/math] at random from the

interval [math][0,1][/math] with uniform density. Find the probability that

• [math]1/3 \lt B \lt 2/3[/math].
• [math]|B - 1/2| \leq 1/4[/math].
• [math]B \lt 1/4[/math] or [math]1 - B \lt 1/4[/math].
• [math]3B^2 \lt B[/math].