Linked Questions

0
votes
1answer
77 views

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 ...
2
votes
1answer
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 ...
1
vote
0answers
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?
111
votes
8answers
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. ...
18
votes
2answers
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?
9
votes
5answers
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?
5
votes
2answers
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 ...
11
votes
2answers
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 ...
2
votes
2answers
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 ...
5
votes
1answer
188 views

Probability that a stick randomly broken in three places can form a triangle

I like questions about geometric probability, and two of my favourite questions here on math.SE are Probability that a stick randomly broken in two places can form a triangle and Probability that a ...
0
votes
1answer
85 views

Probability of a piece of stick being a certain size?

Suppose Alex has a one meter long wooden stick that Alex breaks randomly in two places such that the location of the breaks are independently distributed uniformly along the length of the wooden stick....