Suppose a dart lands at random on the dartboard.Find the probability that the dart will land in the purpleregion.Four rings to dart board inner ring is green, then the next out ispurple, then the next is green, then the outer/last one ispurple.The width of each ring = 2 in.r = 2 in (inner most circle)The answer is 62.5% WHY?

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Terry Avery · Accepted Answer

The rings are of radius 2, 4, 6, and 8 inches. Each ring is anannulus, i.e., a large circle with a smaller circleremoved.The area of the inner purple region is .   π  (      4    2    −      2    2    )  =  12  πThe area of the outer purple region is   π  (      8    2    −      6    2    )  =  28  π.Thus, the total purple area is  40  π .The area of the entire target is   π  (      8    2    )  =  64  π.Since the darts land randomly, the probability of landing inpurple is the ratio of the area of the purple to the total area:   P  =            40      π              64      π        =      5    8  .

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