A missing helicopter is reported to have crashed somewhere in the rectangular region as shown in the figure. What is the probability that it crashed inside the lake shown in the figure?

Step 1: Calculate the area of the entire region of the figure and area of the lake
Area of the rectangular region
length = 9 km
breadth = 4.5 km
Area = length * breadth = 9 * 4.5 = 40.5 km^2
Area of the lake
length = 4.5 - 2 = 2.5 km^2
Breath = 9 - 6 = 3 km^2
Area = 2.5 * 3 = 7.5 km^2
Step 2: Identify the sample space and favourable outcomes
The sample space = The entire area of the rectangular region where the helicopter can crash = 40. 5 km^2
The favourable area to crash helicopter inside the lake = Area of the lake = 7.5 km^2
Therefore, P (helicopter crashed in the lake) = \frac{7.5}{40.5}
= \frac{75}{405}
= \frac{5}{27}