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The probability depends on the nature of the outcomes in the set: whether or not they are mutually exclusive, independent.
If A and B are mutually exclusive event then Probability of A or B is P(A)+P(B). If they are not mutually exclusive then it is that minus the probability of the P(A)+P(B) That is to say P( A or B)= P(A)+P(B)- P(A and B). Of course it is clear that if they are mutually exclusive, P(A and B)=0 and we have the first formula.
Two events that cannot occur at the same time are called mutually exclusive. If two events are mutually exclusive what is the probability that both occur.
Mutually exclusive events are considered two events that cannot coexist with one another, in other words, if the first event is happening the second just cannot. Determining the probability for mutually exclusive events can be done by using the formula P ( A and B ) = 0.
In probability, the probability of the occurrence of event A or event B is the sum of their probabilities only if they are mutually exclusive; not otherwise. So, by itself, "or" does not mean anything.