Question

A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.

Answer 1

Suppose the square has side lengths of 2. Then its area is 2² = 4.

The radius of the circle is 1, so its area is π·1² = π.

The area of the square not in the circle is 4 - π, so the fraction of the area of the square that is not in the circle is

... (4-π)/4 = 1-(π/4) ≈ 0.2146

This same fraction is your probability of selecting a point in the white area.