probability - 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?

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

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}