Question

A point is selected at random from the interior of a circle. The probability that the point is closer to the centre than the boundary of the circle is

• A. $\frac{3}{4}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. none of these

Answer 1

The correct option is C $\frac{1}{4}$

consider the radius of circle as r, then the points closer to center than boundary will lie within the radius of r/2. So the favorable outcomes would be the points inside the area of circle with radius r/2, whereas the total possible outcomes would be all the points inside the area of circle with radius r.

Therefore the probability is $P\left(E\right)=\frac{\pi r^2/4}{\pi r^2}$$=\frac{1}{4}$