Geometrical probability (part 3)

Geometry Level 3

Two points A A and B B are randomly selected from the circumference of a circle with centre O O and radius 1 cm. Find the probability that the the area of sector O A B OAB is greater than 1 cm 2 ^2 . Express your answer correct to 5 decimal places.

Part 1 .

Part 2 .


The answer is 0.36338.

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1 solution

Take note that the area of a sector is 1 if and only if A O B = 2 r a d \angle AOB = 2 rad . Also, take note that sector AOB is formed if the angle is in anti-clockwise direction or clockwise direction. Thus the probability required is 1 2 π 1 - \frac{2}{\pi} .

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