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In the given figure, A, B, C and D are c...

In the given figure, A, B, C and D are centres of four circles that have a radius of 1 unit. If a point is selected at random from interior of square ABCD, then what is the probability that it lies in the shaded region

Text Solution

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Here, Side of the square`ABCD = 2**1 = 2` units
`:.` Area of square `ABCD (A_1)= 2^2 = 4` square units
Now, area of the shaded region `(A_S) = A_1-4**(pir^2)/4`
`=>A_S = 4-pi(1)^2 = 4-pi`
So, the required probability `= A_S/A_1 = (4-pi)/4 = 1-pi/4`.
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