A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16ft2. The hole has a diameter of 1 ft. What is the probability of hitting a ball into the circular hole?

Express your answer as a percentage rounded to the nearest tenth.

Use a kind of probability which is called a geometric region probability. This is defined as

P = (measured of region in the event) / (measured of entire region)

The area of the entire region (circle) is given: 16 ft²

The area of the circular hole is A = πd²/4 = π (1) ²/4 = π/4 ft²

Hence, the probability is

P = (π/4) / 16 = 0.05 = 5%