Landing near the fence of a field

Question

A seed is scattered onto a rectangular field measuring 30 m by 20 m, landing at a uniformly random point. What is the probability that it lands within 5 m of the boundary fence?

Accepted Answer

Points more than 5 m from every side form an inner rectangle reduced by 5 m on each side: (30 - 10)(20 - 10) = 20 	imes 10 = 200 	ext{ m}^2 . The field has area 30 	imes 20 = 600 	ext{ m}^2, so the interior fraction is 	frac{200}{600} = 	frac13 and P(	ext{within 5 m of the fence}) = 1 - 	frac13 = 	frac23 . Takeaway. With a strip width that is a large fraction of the field, most of the area is near the edge. Always compute the interior (L - 2w)(W - 2w) and subtract.

Landing near the fence of a field

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