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