If an ant runs randomly through an enclosed
circular field of radius 2 feet with an inner circle of
radius 1 foot, what is the probability that the ant will
be in the inner circle at any one time?
a. 1/8
b 1/6
c 1/4
d. 1/2
e 1

The area of a circle is π (radius²)

The area of the outer (2-ft) circle is π (2²) = 4 π square feet.

The area of the inner (1-ft) circle is π (1²) = 1 π square feet.

The inner circle covers 1/4 of the area of the outer circle.

So if the ant wanders around totally aimlessly and randomly, and there’s no way to
know where he came from, where he is now, or where he’s going next, and there’s
an equal chance of him being anywhere in the big circle at any time, then there’s a
25% chance of him being inside the small circle at any time, because 1/4 of the
total area is in there.

That’s choice c).