If a line segment is cut into 3 parts, what is the probability that those 3 parts can form a triangle ?

Question

hartnn · Answer

50% ??

mayankdevnani · Answer

For example, if I have a length of rope 10.
I can cut it into 1-1-8 (no triangle)
Or 2-3-5 (no triangle)
Or 4-4-2 (triangle)
Or 3-3-4 (triangle).

mayankdevnani · Answer

just apply triangle inequality.

hartnn · Answer

your point is , 
sum of two sides of triangle must be > 3rd ?

mayankdevnani · Answer

yaaa

hartnn · Answer

used that, solved it, got 50% 
want to verify whether its correct....

mayankdevnani · Answer

verify-
3,3,3(forms triangle)
sum of two sides of triangle must be > 3rd(6>3)

hartnn · Answer

i would like to restate :
sum of two sides of triangle must be > or = 3rd

mayankdevnani · Answer

right

mayankdevnani · Answer

6>3(3+3>3) PROVE IT!

mayankdevnani · Answer

thus, it proves it forms a triangle!!!
@hartnn  can you understand??

hartnn · Answer

yes, that forms equilateral triangle. but i want to find the probability.

mayankdevnani · Answer

i think probability is outcome/parts=10/3

hartnn · Answer

probability can never be >1  -_-

anonymous · Answer

You want that 1 of the segments is not >0.5 of the stick.

anonymous · Answer

I think the probability here may be dependent on the decision procedure that you choose the 3 parts in. Can I assume you throw 2 darts simultaneously at the stick, and these points are the points that you cut it?

hartnn · Answer

even i can't say what can be assumed, this was the question...and i found it mathematically that this probability is 50% , just want to see new approaches and verify my answer.
so , go ahead and try it...

anonymous · Answer

Well, using my method it's less than 50% that form a triangle.

Call where the first dart lands X|dw:1354373456702:dw|, in the half of the stick called A Disregard the 'A' half of the stick. Now, the chance that the second dart lands in A, leaving there a segment of >0.5 is 50%.

However...

anonymous · Answer

It is possible that the second dart lands in B AND the second dart lands in A  AND STILL there would be 1 segment >0.5 length of the stick.|dw:1354373603207:dw| So the chance of a non-triangle, because of this, is LESS than 50%.

But it absolutely matters which procedure you use to cut.