(a) A stick is broken into three pieces by picking two points independently and
Chapter 7, Problem 14(choose chapter or problem)
(a) A stick is broken into three pieces by picking two points independently and uniformly along the stick, and breaking the stick at those two points. What is the probability that the three pieces can be assembled into a triangle? Hint: A triangle can be formed from 3 line segments of lengths a, b, c if and only if a, b, c 2 (0, 1/2). The probability can be interpreted geometrically as proportional to an area in the plane, avoiding all calculus, but make sure for that approach that the distribution of the random point in the plane is Uniform over some region. (b) Three legs are positioned uniformly and independently on the perimeter of a round table. What is the probability that the table will stand?
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