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27 July, 19:06

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.

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  1. 27 July, 20:31
    0
    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%
  2. 27 July, 21:25
    0
    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%
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