Let [math]x[/math] and [math]y[/math] be chosen at random from the interval [math][0,1][/math]. Which pairs of the following events are independent?

• [math]x \gt 1/3[/math].
• [math]y \gt 2/3[/math].
• [math]x \gt y[/math].
• [math]x + y \lt 1[/math].