Contains the Center? 4

Probability Level pending

Choose six points randomly and uniformly on a circle. Let these points be the vertices of a hexagon. What is the probability that the center of the circle lies in this hexagon?


The answer is 0.812.

Christopher Criscitiello by Christopher Criscitiello , 25, USA

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1 solution

Arjen Vreugdenhil
Dec 19, 2017

The answer is 1 − 6 × ( 1 2 ) 5 = 13 16 ≈ 0.8125 1 - 6\times (\tfrac12)^5 = \frac{13}{16} \approx \boxed{0.8125} . For an explanation, adjust my solution to this variant .

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