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

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1027

1126

527

926

answer is C.

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Detailed Solution

Given that a helicopter has crashed somewhere in the rectangular region.
We need to find the probability that it crashed inside the lake.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

The probability that the helicopter has crashed inside the lake will be computed as:

P (E) = area of lake total area of rectangle

For the whole rectangle, we have,
Length = 9km
Breadth = 4.5km
Area of the rectangle is given by:
Area 1 = length

×

breadth

⇒ Area 1 = 9 × 4 .5

⇒ Area 1 = 9 × 92

⇒ Area 1 = 812 k m 2

For the lake, we have,
Length = (9 - 6) km

⇒

Length = 3km
Breadth = (4.5 – 2) km

⇒

Breadth = 2.5km
Area of the lake is given by:
Area 2 = length

×

breadth

⇒ Area 2 = 3 × 2. 5

⇒ Area 2 = 3 × 52

⇒ Area 2 = 152 k m 2

Probability that the helicopter has crashed inside the lake is given by:

P (E) = 152812 ⇒ P (E) = 1581 ⇒ P (E) = 527

Hence, the probability that helicopter has crashed inside the lake is

527

.
Therefore, option 3 is correct.

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