Browse · harp
Printsmc
counting and probability senior
Problem
Three numbers in the interval are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area?
(A)
(B)
(C)
(D)
Solution
Because we can let the the sides of the triangle be any variable we want, to make it easier for us when solving, let's let the side lengths be and . WLOG assume is the largest. Then, , meaning the solution is , as shown in the graph below.
Final answer
C