Question

A football is kept inside a circular field. What is the probability of this ball being closer to the centre of the circle than to the periphery of the ground?
A. Radius of the circular field is 15 m.
B. Radius of the football is 5 cm.
C. Ratio of circumference and diameter of the circle is constant.

• A. Mark (a): if the question can be answered by using any two statements together but not by using any statement alone
• B. Mark (b): if the question can be answered by using either of the statements alone.
• C. Mark (c): if the question can be answered only by using all the three statements together and neither by any pair of statements nor by any statement independently.
• D. Mark (d): if the question cannot be answered using the statement in any case.
• E. Mark (e): if none of the above four options are correct.

Answer 1

The correct option is E

Mark (e): if none of the above four options are correct.

This question can be solved without using any of the statements given.
Football will be closer to the centre than to the circumference if the point is lying in the segment A.
Area of segment $A=\frac{1}{4}\pi r^2$

So, probability of point being closer to the circumference $=\frac{\frac{1}{4}\pi r^2}{\pi r^2}=\frac{1}{4}$
[The probability of ball being closer to the centre = $\frac{\text{Area of the smaller circle inside}}{\text{Area of the larger circle}}$ $=\frac{A}{(A+B)}=\frac{1}{4}]$