A number [math]U[/math] is chosen at random in the interval [math][0,1][/math]. Find the probability that

• [math]R = U^2 \lt 1/4[/math].
• [math]S = U(1 - U) \lt 1/4[/math].
• [math]T = U/(1 - U) \lt 1/4[/math].