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 16π ft2. 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.

Answer: 5

Step-by-step explanation: 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%

1.6%

Step-by-step explanation:

The hole has a diameter of 1 ft, or a radius of ½ ft. The area of the hole is:

A = π r²

A = π (½ ft) ²

A = ¼π ft²

The probability is therefore:

(¼π ft²) / (16π ft²)

1/64

≈ 1.6%