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Probability of their's constituting a triangle? [duplicate]

We have a line segments with length $l$ then you choose two random points and cut it from these points so that we have three piece of line segments. What is the probability that these piece ...
56 views

Building a triangle from random segments [duplicate]

The problem Let's consider the interval $[0, 1]$. We break this interval randomly in two parts. Then we choose the bigger part and again we break it randomly into two parts. At the end we have three ...
53 views

Forming a triangle probabilistically [duplicate]

What is the probability that if you break a stick at $2$ points the three sides form a triangle? Is there a technique that avoids calculus?
5k views

Probability that a stick randomly broken in five places can form a tetrahedron

Edit (June. 2015) This question has been moved to MathOverflow, where a recent write-up finds a similar approximation as leonbloy's post below; see here. Randomly break a stick in five places. ...
5k views

Probability that the convex hull of random points contains sphere's center

What is the probability that the convex hull of $n+2$ random points on $n$-dimensional sphere contains sphere's center?
2k views

expected area of a triangle determined by randomly placed points

Three points are placed at independently and at random in a unit square. What is the expected value of the area of the triangle formed by the three points?
1k views

Probability that a triangle can be formed from a permutation of three edges of random length

What is the probability that a particular set of integer edge lengths selected from an interval $[1, N]$, can form a triangle? How might this extend to the case where one selects real number edge ...
401 views

A samurai cuts a piece of bamboo

Suppose a samurai wants to try out his new sword and cuts a piece of bamboo twice, randomly, so now there are $3$ lenghts of bamboo. What is the probability of these 3 pieces being able to form a ...
462 views

What is the probability for a wood stick of real number length breaking in three piece that can forming precisely a triangle?

What is the probability for a wood stick of any real number length breaking in three piece that can forming precisely a triangle without any extra segment extend from the side of the triangle? My ...