Question

Find the probability that a randomly chosen point is in the shaded area

Answer 1

probability = area of shaded part / area of the large circle

Answer 2

area of shaded bit = area of 'middle' circle pi*4^2 - area of small circle (pi8 2^2)

Answer 3

* pi*2^2

Answer 4

area of large circle = pi*6^2

Answer 5

The orange annulus has an inner radius of 2 and an outer radius of 4 so its area is given by \(\pi R^2-\pi r^2=\pi(4^2-2^2)=12\pi\). Assuming a uniform probability distribution that ensures all points in our disk are chosen with equal likelihood, consider the total area of our disk \(\pi(62)=36\pi\) and our probability can be computed \(12\pi/36\pi=1/4\)