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The probability that all three pairwise distances between the points are less than the radius of the circle is 1/12.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Since it doesn't matter where the first point is picked, it can be placed anywhere on the circle.
The following point must be within an arc of 60 degrees on either side, providing a total of 120 degrees and a chance of 1/3. The final point must be situated within 60 degrees of the first two.
If the first two points are apart by 60 degrees, the third point can be placed within an arc with a minimum area of freedom of 60 degrees and a chance of 1/6. If the first two points are the same, the third point can be placed with a maximum degree of freedom of a 120 degree arc and a 1/3 probability.
The chance changes linearly with increasing distance from the first point, up to a maximum of 60 degrees.
As a result, we may find 1/4, the average likelihood we can position the third point based on a fluctuating second point, by averaging the probabilities at either end.
Total probability is 1 × 1/3 × 1/4 = 1/12.
To learn more about randomly and independently, click on below link:
https://brainly.com/question/13488890
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