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3 points are randomly drawn on a circle. what is the probability of them being on the same semi-circle ?

User Wookiekim
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1 Answer

5 votes

Answer:

3/4

Explanation:

There are 3 Points A,B,C. The first point can be anywhere on the circle Let’s define it to be A. Let’s now orient the circle so that A is the top most point of the circle.Now imagine the circle to be cut in half vertically (into 2 semicircles, where A is in both semicircles) The next two points should be both clockwise or counterclockwise of point A, for the sake of counting lets choose clockwise. There is a 12∗12=1412∗12=14 probability that B and C are on the clockwise side of the semicircle. But the first point could have been A B or C so multiplying by 3 the answer is 3/4

User Kanchan
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