Question

In figure $A,B,C$ and $D$ are centre of 4 circles that each have a radius of length one unit. If a point is selected at random from the interior of a square $ABCD$. Then the probability that it will be chosen from shaded region is

• A. $(1-\frac{\pi }{12})$
• B. $(1-\frac{\pi }{2})$
• C. $(1-\frac{\pi }{6})$
• D. $(1-\frac{\pi }{4})$

Answer 1

The correct option is D $(1-\frac{\pi }{4})$

Side of square $=2$ unit
Area of square $=2^2$ sq unit = $4$ sq unit
Area of shaded region $=$ Area of square $-$ Area of circle
$=2\times 2-4\times \frac{\pi (1{)}^2}{4}=4-\pi$
$P($point chosen from inside the region$)$
$=\frac{4-\pi }{4}=(1-\frac{\pi }{4})$