If we select a random point in a circle of 1 unit radius, what is the probability that the point is closer to the circumference than to the center?

Question

Accepted Answer

Probability of a random point in a circle of 1 unit radius being closer to the circumference than the center.

The probability is 1/4 or approximately 0.785.
This is because the area of the circle closer to the circumference is 1/4th of the total area.
This can be calculated using the formula for the area of a circle: A = πr^2.

Accepted Answer

(Radius/2) divides the centre and circumference.

Total area = π * r *r

Probability of a point appearing inside the circle is 1.

Probability of a point appearing closer to the circumference means it should appear in the region between (radius/2 ) point and circumference point.

Imagine a circle with new radius = original circle radius / 2.

For the condition to satisfy the point should appear out of this smaller circle.

Probability = 1 - (area of new circle/ area of original circle) .

Answer is 1- {(π × 0.5 × 0.5) / π } = 0.75

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