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Math Help - Circle probability

  1. #1
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    Circle probability

    Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn, one inside the other, dividing the circle of radius 5 into five regions: a circle of radius and 4 annuli (rings). What is the probability that a point chosen randomly from within the circle of radius 5 lies in the annulus whose inner radius is 3 and whose outer radius is 4? Can someone tell me if this is the right answer? i got a 7/25 chance. THanks!
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  2. #2
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    Hello, jarny!

    You're correct . . . Nice work!

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    Re: Circle probability

    How? could you explain. i need help with the same question. thank you.
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  4. #4
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    Re: Circle probability

    Hello, mmathh!

    Five concentric circles with radii 1, 2, 3, 4, and 5 are drawn, one inside the other,
    dividing the circle of radius 5 into five regions: a circle of radius 1 and 4 annuli (rings).

    What is the probability that a point chosen randomly from within the circle of radius 5
    lies in That Ring whose inner radius is 3 and whose outer radius is 4?

    The total area is: . A \:=\:\pi r^2 \:=\:\pi(5^2) \:=\:25\pi


    The circle with radius 4 has area: . \pi (4^2) \,=\,16\pi
    The circle with radius 3 has area: . \pi(3^2) \,=\,9\pi

    The area of That Ring is: . 16\pi - 9\pi \,=\,7\pi


    Therefore: . P(\text{point is in That Ring}) \:=\:\frac{7\pi}{25\pi} \:=\:\frac{7}{25}

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