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What is the probability that all lie in the same semicircle if n points are chosen randomly on the
circumference of a circle ?
Solution
each point has 2 possibilities - 1. lies in the semi circle 2. doesnt lie....thus probability of lyingg
in semicircle is 0.5 i.e. 1/2 ...hence for n points ,probability of lying in semi circle =n/2^n

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