Expected value of an event which has a probability of occuring

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An event has an expected value of $E$. The probability of the event happening is $P$. What is the total expected value of the event, if the value when the event does not occur is $0$?

For example, say you're playing a game where you score points by rolling a $6$-sided dice, such that the average you could score per roll is $3.5$. But you only get to roll the dice after a certain condition is met. If the condition is not met, you don't roll the dice and you score $0$. So, each round there is a $1-P$ chance of scoring a $0$, and a $P$ chance of scoring (on average) a $3.5$. What would be the total average score per round?

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An event can't have an "expected value"; although the indicator function of an event can.

For your particular question, the expected score of a dice roll here is $$(1-P)\cdot 0 + P \cdot 3.5 = 3.5P.$$