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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#### Solution

Radius of circle = 1cm

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

Area of square = 2 × 2 =` 4cm^2`

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

= 4 – 4 `(1/4) pi(1)^2`

= (4 − 𝜋)` cm^2`

Probability that the point will be chosen from the shaded region =`"Area of shaded regfion"/"Area of square ABCD"`= `(4−pi)/4` = 1 −`(pi/4)`

Since geometrical probability,

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

Concept: Basic Ideas of Probability

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