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Mathematics · JEE | PROBABILITY
हिन्दीBased on the rectangular region containing a lake shown in Fig. 14.2, where dimensions of the rectangle are \( 9\text{ km} \times 4.5\text{ km} \), if a missing helicopter is equally likely to crash anywhere in the region, what is the probability that it crashed inside the rectangular lake whose dimensions are indicated on the figure?
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Correct answer · Option D
4/27
Explanation
Total area = \( 9 \times 4.5 = 40.5\text{ km}^2 \). Lake dimensions: width = \( 9 - 6 = 3\text{ km} \) or from the top right part, length = 3 km, height = 2 km (from 4.5 - 2.5 = 2 km). Area of lake = \( 3 \times 2 = 6\text{ km}^2 \). Probability = \( \frac{6}{40.5} = \frac{12}{81} = \frac{4}{27} \).
