Pick a point [math]x[/math] at random (with uniform density) in the interval [math][0,1][/math]. Find the probability that [math]x \gt 1/2[/math], given that

• [math]x \gt 1/4[/math].
• [math]x \lt 3/4[/math].
• [math]|x - 1/2| \lt 1/4[/math].
• [math]x^2 - x + 2/9 \lt 0[/math].