The rule of addition applies to the following situation. We have two events from the same sample space, and we want to know the probability that either event occurs.

Rule of Addition If events A and B come from the same sample space, the probability that event A and/or event B occur is equal to the probability that event A occurs plus the probability that event B occurs minus the probability that both events A and B occur.

P(A B) = P(A) + P(B) – P(A ∩ B)

Note: Invoking the fact that P( A ∩ B ) = P( A )P( B | A ), the Addition Rule can also be expressed as

P(A ∪”; B) = P(A) + P(B) – P(A)P( B | A )
 
So it’s like the possibility that the space shuttle will burst into flames (A) or fall apart (B) while crashing into the moon?  I think this raises the question of why both can’t happen but maybe that’s a different topic.  I guess it depends on if it’s a scheduled malfunction (referencing Destination: Void by Frank Herbert) .
 
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