We all know that, given two events A and B, the probability of the union A U B is given by the formula P(A U B) = P(A) + P(B) - P( AB) where AB represents the intersection of A and B. Most of us even know that
P(A U B U C) = P(A) + P(B) + P(C) - { P(AB) + P(AC) + P(BC) } + P(ABC)
In particular, if the events are independent, it becomes:
1 - P(A U B U C) = 1 - { P(A) + P(B) + P(C) } + { P(A)P(B) +…