Mathematics

Question

Suppose that all of the points on the circular dartboard shown are equally likely to be hit by a dart. If the radius of the shaded center circle is 1 and the radius of the entire dartboard is 4, what is the probability of throwing a dart and hitting the white part of the board? Round your answer to the nearest whole number.

2 Answer

  • this must double your chances so if i round the nearest whole number would be 8 any questions?
  • Answer: The probability of throwing a dart and hitting the white part of the board is 1.

    Step-by-step explanation:

    Since we have given that

    Radius of shaded center circle = 1

    So, Area of shaded center circle is given by

    [tex]\pi r^2\\\\=\pi \times 1^2\\\\=\pi[/tex]

    Radius of entire dartboard = 4

    Area of entire dartboard is given by

    [tex]\pi\times 4^2\\\\=16\pi[/tex]

    Area of white part is given by

    [tex]16\pi-\pi\\\\=15\pi[/tex]

    So, Probability of throwing a dart and hitting the white part of the board is given by

    [tex]\dfrac{15\pi}{16\pi}\\\\\\=\dfrac{15}{16}=0.9375\approx 1[/tex]

    Hence, the probability of throwing a dart and hitting the white part of the board is 1.

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