GATE CE 2021 Set 2 — Question 9
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General Aptitude → Quantitative Aptitude → Elementary Statistics & Probability
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Question
In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.The probability that any point picked randomly within the square falls in the shaded area is __________
Correct answer
(C) (π)/(2) - 1
Solution
Let the side of the square PQRS be .
Total area of the square = .
The shaded region is the intersection of two quarter-circles (quadrants) of radius , one centered at S and the other at Q.
Area of one quadrant = .
Area of the shaded region = (Area of quadrant centered at S) + (Area of quadrant centered at Q) - (Area of square PQRS)
Area of shaded region = .
The probability that a randomly picked point falls in the shaded area is the ratio of the shaded area to the total area:
.
Total area of the square = .
The shaded region is the intersection of two quarter-circles (quadrants) of radius , one centered at S and the other at Q.
Area of one quadrant = .
Area of the shaded region = (Area of quadrant centered at S) + (Area of quadrant centered at Q) - (Area of square PQRS)
Area of shaded region = .
The probability that a randomly picked point falls in the shaded area is the ratio of the shaded area to the total area:
.
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