Probability of A occurring = P(A) : Probability of B occurring = P(B) : Probability of both A and B occurring = P(A and B) : = P(B and A) = P(A ∩ B) = P(AB) "joint probability" ≤ min(P(A),P(B))
Conditional probabilities:
"Probability that a randomly selected 'B' is also a 'A'" "Given that B has occurred, what is the probability that A also occurred" Probability of A given B = P(A|B) = P(A and B) / P(B):
"Probability that a randomly selected 'A' is also a 'B'" "Given that A has occurred, what is the probability that B occurred too" Probability of B given A = P(B|A) = P(B and A) / P(A):
If P(A)=1 and P(B)=1 then P(A and B) must be 1
If P(A)=0 then P(B|A) is undefined If P(B)=0 then P(A|B) is undefined