Problem

如图所示, 在边长为 1 的正方形 $O A B C$ 中任取一点 $M$, 则点 $M$ 恰好取自阴影部分的概率为

Answer

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Answer

\(\boxed{0.5}\)

Steps

Step 1 :Let's find the area of the shaded region. The shaded region consists of two right triangles and a square. The right triangles have legs of length \(\frac{1}{2}\), and the square has a side length of \(\frac{1}{2}\).

Step 2 :Calculate the area of one right triangle: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\).

Step 3 :Calculate the area of the square: \(\left(\frac{1}{2}\right)^2 = \frac{1}{4}\).

Step 4 :Calculate the total shaded area: \(2 \times \frac{1}{8} + \frac{1}{4} = \frac{1}{2}\).

Step 5 :Calculate the probability of point M lying in the shaded region: \(\frac{\text{shaded area}}{\text{total area}} = \frac{\frac{1}{2}}{1}\).

Step 6 :\(\boxed{0.5}\)

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