A point in the figure is chosen at random. Find the probability that the point lies in the shaded region.

Question

here's the graph

Answer 1

Hi Nehemiah,

the area of a circle is pi r ^2.

so the entire circle is 9^2 as the diameter is 18 and radius is one half of the diameter. So the area is 81 pi.

the inner circle is 49 pi. Again 7 is one half of 14.Subtracting 49pi from 81pi which is 31 pi. Then the probability of a point in the shaded area is 31pi/81pi or 31/81.

I hope this helps.

Answer 2

The probability is proportional to the area. The area of the shaded region is the area of the large circle - area of the small (unshaded) circle = π•9² - π•7² = 81π - 49π = 32π. The probability of the point being in the shaded region is then 32π/81π = 32/81 ≈ 39.5%