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}