Find the probability that a point chosen at random in the figure lies in the shaded region. Figure: http://www.flickr.com/photos/93084714@N07/8624620295/
The figure is that of a square with side 10 cm in which lie two semi-circles with radius 5 cm. The area of the shaded region is the difference of the area of the square and that of the circle. This is equal to `10^2 - pi*5^2` .
The probability that a random point chosen in the figure lies in the shaded area is the ratio of the area of the shaded region divided by the area of the square. This is `(10^2 - pi*5^2)/100 ~~ 0.2146`
The required probability is approximately 21.46%