I want to study probability for programming contests someone can help me? like saying a book or a tutorial.
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Probably this can help you
A rule of thumb:
If there is word "probability" or "expected value" in the problem statement, then the solution probably uses dynamic programming.
And probably regards probability.
But I'm curious though, is for every dynamic programming solution there's one equivalent close-form mathematical formula?
No.
look like this problem Ilya and Escalator