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Probability question (of archery target radius)?

An archery target has rings of radius r, 2r, and 3r. Suppose an arrow hits the target randomly. What is the probability that an arrow hits the target will land in each ring?

area of target = π*(3r)^2 = 9πr^2
area of outer ring = 9πr^2 – 4πr^2 = 5πr^2
area of middle ring = 4πr^2 – πr^2 = 3πr^2
area of inner ring = πr^2

P[hit any particular ring] = area of that ring / area of target, so

P[hit inner ring] = 1/9
P[hit middle ring] = 3/9 = 1/3
P[hit outer ring] = 5/9

This entry was posted on Wednesday, May 26th, 2010 at 12:03 pm and is filed under archery target. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “Probability question (of archery target radius)?”

  1. M3 says:
    May 26, 2010 at 5:28 pm

    area of target = π*(3r)^2 = 9πr^2
    area of outer ring = 9πr^2 – 4πr^2 = 5πr^2
    area of middle ring = 4πr^2 – πr^2 = 3πr^2
    area of inner ring = πr^2

    P[hit any particular ring] = area of that ring / area of target, so

    P[hit inner ring] = 1/9
    P[hit middle ring] = 3/9 = 1/3
    P[hit outer ring] = 5/9
    References :

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