QM Probability Concepts

Question 1

Odds

Answer 1

Probability of Y / Probability of not Y

Odds = Y / (1-Y)

Question 2

Odds for E

Answer 2

Odds for E = P(E)/[1 − P(E)]

Question 3

Odds against E

Answer 3

Odds against E = [1 − P(E)]/P(E)

Question 4

Definition of Conditional Probability.

Answer 4

The conditional probability of A given that B has occurred is equal to the joint probability of A and B divided by the probability of B (assumed not to equal 0).

Question 5

Conditional Probability Formula

Answer 5

P(A | B) = P(AB) / P(B)

P(B) ≠ 0

Question 6

Conditional Probability Formula multiplication rule.

Answer 6

P(AB) = P(A | B) * P(B)

Question 7

Conditional Probability Formula multiplication rule.

Answer 7

P(AB) = P(BA) = P(B | A) * P(A)

Question 8

Addition Rule for Probabilities

Answer 8

P(A or B) = P(A) + P(B) – P(AB)

Question 9

Multiplication Rule for Independent Events

Answer 9

P(AB) = P(A) * P(B)

Question 10

Total Probability Rule.

2

Answer 10

P (A) = P(AS) + P(AS^c)

= P (A | S ) * P(S) + P(A | S^c) *P(S^c)

Question 11

Total Probability Rule

n

Answer 11

P (A) = P(AS₁) + P(AS₂) + … + P(AS_n)

= P (A | S₁ ) * P(S₁) + P(A | S₂) * P(S₂) + … + P(A | S_n) * P(S_n)