Question

In the figure, all the four shaded semicircles have same area. If we put a dot in the figure without looking into it, what is the probability of being the dot in the shaded semicircles?

Answer 1

If the radius of the shaded semicircle is r,

Area of all semicircles = \(4\times\frac{\pi r^2}{2}=2\pi r^2\)

Area of the bigger circle = \(\pi(4r)^2=16\pi r^2\)

Probability = \(\frac{2 r^2}{16 r^2}=\frac{1}{8}\)