Question

HELP MEEEEE!!!

What is the probability that a point chosen at random in the given figure will be inside the larger circle and outside the smaller circle?


Enter your answer, as a fraction in simplest form, in the box.

P(inside larger circle and outside smaller circle) = _____


I know the answer is 40/49, but I don't know how. Please explain how you get the answer. Thank you!

Answer 1

So first, let us say that the inner circle is circle B and the outer circle is circle A. The area of circle A minus the area of circle B gives you the area between them. So, the area of circle A is 14²π = 196π. The circle B's area is 6²π = 36π. Hence, the area is 160π between both of them. Now, the area of the outer circle as we found is 196π, so the probability that I would choose a point between the outer and inner circle is 160π/196π = 40/49.