A point [math]P[/math] in the unit square has coordinates [math]X[/math] and [math]Y[/math] chosen at random in the interval [math][0,1][/math]. Let [math]D[/math] be the distance from [math]P[/math] to the nearest edge of the square, and [math]E[/math] the distance to the nearest corner. What is the probability that

• [math]D \lt 1/4[/math]?
• [math]E \lt 1/4[/math]?