3. (7 points) From the airplane window, I can see part of an island, part of a cloud, and a bit of the sea. The cloud occupies half of the landscape visible from the window and thus hides a quarter of the island, which therefore takes up only a quarter of the observed landscape. What part of the landscape does the part of the sea hidden by the cloud constitute?

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# Solution.

![](https://cdn.mathpix.com/cropped/2024_05_06_7d1f430bf2ead38662c6g-2.jpg?height=403&width=403&top_left_y=244&top_left_x=901)

Three quarters of the island occupy a quarter of the landscape visible through the porthole. Therefore, the entire island constitutes $\frac{1}{3}$, and the sea constitutes $-\frac{2}{3}$ of the visible landscape. The part of the sea not covered by clouds is $\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$ of the landscape. Therefore, the portion of the sea hidden by clouds is $\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$ of the landscape.

Answer. $\frac{5}{12}$.