expected cost per year for a given event and probability

[Marbles99]

Dear forum experts,

given is an event X with probability of occurrence P(X)=0.2 per year. When the event occurs it leads to a cost of 6,000$. I am looking for a way to answer the question what is the expected cost of the event per year, i.e. E(X).

My question:
Under what conditions can I calculate the expected value as E(X)=P(X)*cost? Does it need a certain distribution like the normal distribution as an assumption? Or some other condition to be able to use this formula?

 

[HallsofIvy]

You don't need to "assume" any distribution! You are TOLD that the distribution is binary with P(X)= 0.2.

 

[JeffM]

Expected value is the sum over all events of value of the event occuring times the probability of the event occuring.

What are the events, what are their costs, what are their probabilities?