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What is the definition of a "success" in a binomial setting?
In a Binomial setting, there are only two possible outcomes per try. Depending on what you want, you call one of the possibilities Fail and the other one Succes.
Example : You may call rolling a 6 with a die Succes, and a non-6 a Fail. Depending on the conditions of the game, rolling a 6 may cost you money, and you may want to reverse the terms.
In short: There are only two possible outcomes per try, and you may name them as you want: White-Black, Heads-Tails, whatever. Usually the one you use as ##P## in calculations is called (probability of) Succes.