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Question
A missing helicopter is reported to have crashed somewhere in the rectangular region shown in the figure. What is the probability that it crashed inside the lake shown in the figure?
Solution
The helicopter is equally likely to crash anywhere in the region. In the figure, the length and the breadth of the rectangle are 9 m and 4.5 m respectively.
Area of the entire region where the helicopter can crash
= (9 × 4.5) m2 = 40.5 m2
Let A be the event that helicopter crashed inside the lake.
The lake is rectangular shaped.
Length of lake = 9 – 6 = 3 m
Breadth of lake = 4.5 – 2 = 2.5 m
Area of lake = length × breadth
= 3 × 2.5
= 7.5 m2
∴ P(A) = `("n"("A"))/("n"("S"))`
= `7.5/40.5`
= `75/405`
= `5/27`
The probability that the helicopter crashed inside the lake is `5/27`
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