The user-friendly version of this content is available here.

The following content is copyright (c) 2009-2013 by Goods of the Mind, LLC.

This problem trains for: SAT-I, AMC-8, GMAT.

In the county of San Matheo, homes are rated as class 4 if they are no farther than 5 miles from a fire station and as class 3 if they are no farther than 2 miles from a fire station. Given a fire station and the homes that surround it, what is the probability that, if a fire breaks at a home, it is a home rated class 4?

The homes that are no farther than 5 miles from the fire station are in a circle of radius 5 with area:

equation

The homes that are rated class 4 are in the circular ring between the circle of radius 2 and the circle of radius 5. The area of this circular ring is:

equation

The probability for a home to be in this circular ring is:

equation