Safely away from every edge

Question

A drop of water lands at a uniformly random point on a tray measuring 16 in by 12 in. What is the probability that it lands more than 2 in from every edge?

Accepted Answer

The favorable region is the inner rectangle, each side pulled in by 2 in: (16 - 4)(12 - 4) = 12 	imes 8 = 96 	ext{ in}^2 . The tray area is 16 	imes 12 = 192 	ext{ in}^2, so P(	ext{more than 2 in from every edge}) = \frac{96}{192} = \frac12 . Takeaway. When the question asks for the interior directly, you keep the inner-rectangle area rather than subtracting it. The interior is (L - 2w)(W - 2w) over the full area.

Safely away from every edge

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