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

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).

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