Triangle ABC is stuck in a circle. Its points are on random areas on the circumference of the circle. What is the probability of the triangle covering the centre of the circle?
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Three points are selected at random on a sphere's surface. What is the probability that they all lie in the same hemisphere? Assume that the great circle, bordering a hemisphere, is part of the hemisphere.
I have a stick of length 3 cm and I select 2 random points on it and break it at those points to get 3 pieces.
If the probability that these pieces will form a triangle is m/n where m and n are coprime integers then what is the value of m × n?
There is an equilateral triangle and three bugs are sitting on the three corners of the triangle. Each of the bugs picks up a random direction and starts walking along the edge of the equilateral triangle. What is the probability that none of the bugs crash into each other?
