Question

There is a point inside a circle,. What is the probability that this point is close to the circumference than to the centre?

• A. $\frac{3}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{1}{3}$

Answer 1

Answer: (A)

$\frac{3}{4}$

For point to be close to the circumference than to the centre the point must be at a distance greater then r/2 from the centre of circle where r is the radius

Area of region of a point such that distance is greater then r/2 from the centre of circle =$\Pi r^2$-$\Pi {\left(r/2\right)}^2$=$3\Pi r^2$/4

Probability that this point is close to the circumference than to the centre=($3\Pi r^2$/4)/$\Pi r^2$=3/4