I know what you mean by the sentence, but it sounds very unnatural. A "supposition" is a guess or hypothesis made with evidence. I see the word used mostly in scientific writing and also in formal writing. For your sentence, I would say "Do you have any idea what could have been the reason for this tragedy?"
A sentence along the same lines may be "The idea that this tragedy could have been prevented is based on the supposition that he/she was willing to take the proper precautions."
"Supposition" is a good word to know, but you will only see it infrequently. Sentences beginning with "Do you have any idea why..." or "Can you guess why..." will be much more common. Hope this helps, J