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Three Points in a Square (Posted on 2008-03-17) Difficulty: 3 of 5
Three points are chosen at random inside a square. Each point is chosen by choosing a random x-coordinate and a random y-coordinate.

A triangle is drawn with the three random points as the vertices. What is the probability that the center of the square is inside the triangle?

No Solution Yet Submitted by Brian Smith    
Rating: 3.2000 (5 votes)

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re(2): Not faster, simpler, or better | Comment 11 of 18 |
(In reply to re: Not faster, simpler, or better by ed bottemiller)

If points are chosen randomly within or on the square, the probability is zero that they would be on (rather than within) the square as the perimeter of the square has zero area.

Likewise the probability that a side of the triangle would go exactly through the center, as again, the lines making the triangle have zero area.

  Posted by Charlie on 2008-03-18 10:45:45

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