I cheated and found the answer googling "stick 3 part triangle" :
https://www.quora.com/A-rod-is-broken-into-three-parts-what-is-the-probability-that-the-three-parts-can-be-arranged-to-form-a-triangle
The answer is: 25%
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haha yes it is :)
took me a long time thinking it over to get it right