In below Fig., points A, B, C and D are the centers of four circles th

1.	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?
Answer» 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)

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?

Answer»

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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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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