1. Probability Rules Rule 1.
The probability of any event (A) is a number between zero and one.
0 < P(A) < 1

2. Probability Rules Rule 2.
The sum of the probabilities of all basic outcomes in the sample space must equal one
P(S)=P(e1)+P(e2)+P(e3)+....+P(en)=1

3. Probability Rules Rule 3.
The probability of the union of two basic outcomes is equal to the sum of the probabilities of the individual events
If E1 = (e1, e2, e3)
then, P(E1) = P(e1) + P(e2) + P(e3)

4. Probability Rules Rule 4.
The Complement of an event is the remainder of the sample space beyond the event
P (A) = 1 - P (A)

5. Probability Rules Rule 5.
The Addition Rule describes the probability for the union of two events as the sum of marginal probabilities minus their joint (common) probability
P(A or B) = P(A) + P(B) - P(A and B)

6. Probability Rules Rule 6.
Addition Rule for mutually exclusive events A and B
P(AUB) = P(A) + P(B)
P(A or B) = P(A) + P(B)

7. Probability Rules Rule 7.
Conditional probability for any two events, A and B, is
P (A given B) = P (A and B) / P (B)
where, P (B) is not equal to zero

8. Probability Rules Rule 8.
Conditional probability for independent events, A and B, is
P (A \ B) = P (A), and
P (B \ A) = P (B)

9. Probability Rules Rule 9.
Multiplication rule for two Events, A and B, is
P (A and B) = P (A) * P (B \ A), or
P (B and A) = P (B) * P (A \ B)

10. Probability Rules Rule 10.
Multiplication rule for independent events, A and B, is
P (A and B) = P (A) * P (B)