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. T he 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.
2 answers:
Answer:
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%
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%
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