In the figure, points A, B, C and D are the centres of four circles, each having a radius of length one unit. If a point is chosen at random from the interior of the square ABCD, what is the probability that the point will be choosen the shaded region?

\frac{4 - π}{4}

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2 - π

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1 - π

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\frac{2 - π}{4}

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Solution

The correct option is A $\frac{4 - π}{4}$
Area of the shaded region $=$ Area of the square $- 4 \times$ Area of the sector of the circle
area of a circle $= (2 \times 2) - 4 \times \frac{1}{4} (π) (1)^{2} = 4 - π$
Required probability $= \frac{A r e a o f s h a d e d r e g i o n}{A r e a o f s q u a r e} = \frac{4 - π}{4}$

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In the figure, points A, B, C and D are the centres of four circles, each having a radius of length one unit. If a point is chosen at random from the interior of the square ABCD, what is the probability that the point will be choosen the shaded region?

The correct option is A 4−π4Area of the shaded region = Area of the square −4× Area of the sector of the circlearea of a circle =(2×2)−4×14(π)(1)2=4−πRequired probability=Area of shaded regionArea of square=4−π4