Consider two independent events, A and B. We would say the probability of A and B occurring is:
P(A ∩ B) = P(A) * P(B)
However, what if A is considered a zero probability event? Not an impossibility, but a zero probability event? (Not the empty set)
If this is the case, what can we say about the relationship between P(A) and P(A ∩ B)?
Does P(A) = P(A ∩ B), because P(A) = 0? Or, is P(A ∩ B) < P(A)?
B is not a zero probability event:
P(B) ∈ (0,1)