1. If two events aremutually exclusive(i.e. they cannot occur at the same time), then the probability of them both occurring at the same time is 0. then:P(A and B) = 0andP(A or B) = P(A) + P(B)

2. if two events arenot-mutually exclusive(i.e. there is some overlap) then:P(A or B) = P(A) + P(B) - P(A and B)

3. If events areindependent(i.e. the occurrence of one does not change the probability of the other occurring), then the probability of them both occurring is the product of the probabilities of each occurring. Then:P(A and B) = P(A) * P(B)

4. If A, B and C are not mutually exclusive events, thenP(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)

Either:

P(A or B)= P(A) + P(B) - P(A and B)

Where, P(A and B) = P(A) * P(B)

Neither:

P(Not A and Not B)= P(A') * P(B')

Where, P(A') = 1 - P(A), P(B') = 1- P(B)

Thanks.