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A missing helicopter is equally likely to have crashed anywhere in the rectangular region shown in Fig. 14.2. What is the probability that it crashed inside the lake? 
A$\frac{5}{27}$
B$\frac{2}{9}$
C$\frac{7}{27}$
D$\frac{5}{18}$
Answer & Solution
Correct answer: A. $\frac{5}{27}$
Use area ratio because every point in the region is equally likely. The full rectangle has dimensions $9\text{ km} \times 4.5\text{ km}$, so its area is $40.5\text{ km}^2$. The lake is a rectangle of dimensions $3\text{ km} \times 2.5\text{ km}$, so its area is $7.5\text{ km}^2$. Therefore, the probability is $\frac{7.5}{40.5}=\frac{75}{405}=\frac{5}{27}$.
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