Rule 1: The probability of an impossible event is zero; the probability of a certain event is one. Therefore, for any event A, the range of possible probabilities is: 0 ≤ P(A) ≤ 1
Rule 2: For S the sample space of all possibilities, P(S) = 1. That is the sum of all the probabilities for all possible events is equal to one. Recall the party affiliation above: if you have to belong to one of the three designated political parties, then the sum of P(R), P(D) and P(I) is equal to one.
Rule 3: For any event A, P(Ac) = 1 - P(A). It follows then that P(A) = 1 - P(Ac)
Rule 4 (Addition Rule): This is the probability that either one or both events occur
a. If two events, say A and B, are mutually exclusive - that is A and B have no outcomes in common - then P(A or B) = P(A) + P(B)
b. If two events are NOT mutually exclusive, then P(A or B) = P(A) + P(B) - P(A and B)
Rule 5 (Multiplication Rule): This is the probability that both events occur
a. P(A and B) = P(A) • P(B|A) or P(B)*P(A|B) Note: this straight line symbol, |, does not mean divide! This symbols means "conditional" or "given". For instance P(A|B) means the probability that event A occurs given event B has occurred.
b. If A and B are independent - neither event influences or affects the probability that the other event occurs - then P(A and B) = P(A)*P(B). This particular rule extends to more than two independent events. For example, P(A and B and C) = P(A)*P(B)*P(C)
Rule 6 (Conditional Probability): \(P(A|B)=\frac{P(A \ and \ B)}{P(B)}\) or \(P(B|A)=\frac{P(A \ and \ B)}{P(A)}\)