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In below Fig., points A, B, C and D are the centers of four circles that each have a radius of length one unit. If a point is selected at random from the interior of square ABCD. What is the probability that the point will be chosen from the shaded region?

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Radius of circle = 1cm

Length of side of square = 1 + 1 = 2cm

Area of square = 2 × 2 = 4cm2

Area of shaded region = area of square – 4 × area of quadrant

= 4 – 4(1/4)π(1)2

= (4 − π) cm2

Probability that the point will be chosen from the shaded region = (Area of shaded region)/(Area of square ABCD) = (4 - π)/4 = 1 - π/4

Since geometrical probability,

P(E) = (Measure of specified part of region)/(Measure of the whole region)

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