Suppose you had five sticks of length 1, 2, 3, 4, and 5 inches. If you chose three at random, what is the likelihood tht the three sticks could be put together, tip to tip, so as to form a triangle?

Now suppose you had twenty sticks, of lengths 1 through 20 inches. If you picked three at random, what is the likelihood that the three could be put together, tip to tip, to form a right triangle?

(Assume that a triangle has to have some area)

Found a simpler formula for the probability of forming a triangle with non-zero area with 3 sticks randomly picked out of n:
p=(2n-5)/(4(n-1))
For even n this formula is exact, for odd n a correction term (-1/(8C)) must be added where C is the total number of combinations of 3 sticks (C=n(n-1)(n-2)/6).
The correction term however becomes negligible very rapidly as n grows (<0.01% for n>20), so the formula for even n can be used universally if n is sufficiently large.

Posted by Yevgen on 2003-11-11 17:44:21