Question

A missing helicopter is reported to have crashed somewhere in the rectangular region of dimensions $9km$ by $4.5km$. What is the probability that it crashed inside the lake which is $3km$ by $2.5km$? (The lake is in the rectangular region)

• A. $\frac{7}{27}$
• B. $\frac{3}{27}$
• C. $\frac{4}{27}$
• D. $\frac{5}{27}$

Answer 1

The correct option is D $\frac{5}{27}$

The possibility of the helicopter is equally likely to crash anywhere in the region given in the figure. Area of the entire region where the helicopter can crash is calculated using:

$=(4.5\times 9)k{m}^2=40.5k{m}^2$

Area of the lake $=(2.5\times 3)k{m}^2=7.5k{m}^2$

Therefore, P (helicopter crashed in the lake) $=\frac{7.5}{40.5}=\frac{75}{405}=\frac{5}{27}$