Probability 1
Algebra
Level
pending
An equilateral triangle ABC is drawn along with its circumcircle. Now three points are chosen at random on the circumference of this circle. If the probability that the three points are in the three different arcs AB,BC,CA is P, then write the first three digits of P after decimal.
The answer is 222.
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1 solution
The first point can be anywhere, probability it is there is 1.
The second point has to be in one of two arcs, all the same size, probability 3 2 .
The third point has to be in the only arc left open, probability 3 1 .
Probability of all of these things happening simultaneously is the product 1 ⋅ 3 2 ⋅ 3 1 = 9 2 ≈ 0 . 2 2 2