The probability of the dart hitting the smaller ring is?A dart is randomly thrown at a circular board on which two concentric rings of radii R and 2R having the same width (width much less than R) are marked. The probability of the dart hitting the smaller ring is:(1) Twice the probability that it hits the larger ring.(2) Half of the probability that it hits the larger ring.(3) Four times the probability that it hits the larger ring.(4) One-fourth the probability that it hits the larger ring.

Question

emerhelienapj · Accepted Answer

Step 1Let&#039;s say the common width was W. Then the area occupied by a ring of radius r would be   π  (  r  +  W      )    2    −  π      r    2    =  2  π  r  W  +  π      W    2  Thus the probability that the dart will land in that ring is             2      π      r      W      +      π              W        2                    π              S        2              =            2      r      W              S      2        +            W      2              S      2        ≈            2      r      W              S      2       where we have used the fact that W is much smaller than S.Step 2It follows that the ratio you want is approximately             2      R      W              S      2                  /                  4      R      W              S      2        =      1    2