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प्रश्न
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?
उत्तर
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`
संबंधित प्रश्न
Two-digit numbers are formed from the digits 0,1,2,3,4 where digits are not repeated. Find the probability of the events that:
(a) The number formed is an even number.
(b) The number formed is a prime number.
If one die is rolled, then find the probability of the following event by completing the activity.
Event A: The number on the upper face is prime.
Activity: Let ‘S’ be the sample space.
S = {1, 2, 3, 4, 5, 6}
∴ n(S) = 6
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A = {`square`}
∴ n(A) = 3
P(A) = `square/(n(S))` .....[Formula]
= `square/6`
∴ P(A) = `1/square`
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∴ n(S) = 52
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∴ n(A) = `square`
∴ P(A) = `square/(n("S"))` ......[Formula]
P(A) = `26/52`
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(2) n(S) = `square`
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