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

Probability Rules l Rule 2. The sum of the probabilities of all basic outcomes in the sample space must equal one P(S)=P(e 1 )+P(e 2 )+P(e 3 )+....+P(e n )=1

Probability Rules l Rule 3. The probability of the union of two basic outcomes is equal to the sum of the probabilities of the individual events If E 1 = (e 1, e 2, e 3 ) then, P(E 1 ) = P(e 1 ) + P(e 2 ) + P(e 3 )

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

Probability Rules l 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)

Probability Rules l 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)

Probability Rules l 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

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

Probability Rules l 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)

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