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Pick two points A and B independently at random in a ball with centre O. Show that the probability that the angle AOB is obtuse is . Compare this with the corresponding result for two points picked at random in a circle.

Pick two points A and B independently at random in a ball with centre O. Show that the probability that the angle AOB is obtuse is . Compare this with the corresponding result for two points picked at random in a circle.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Pick two points A and B independently at random in a ball with centre O. Show that the probability that the angle AOB is obtuse is g. Compare this with the corresponding result for two points picked at random in a circle.
Transcribed Image Text:Pick two points A and B independently at random in a ball with centre O. Show that the probability that the angle AOB is obtuse is g. Compare this with the corresponding result for two points picked at random in a circle.
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