Probability formulas

11 flashcards · Mathematics · by J M COOPER

1. Rule of Multiplication (Product rule) P(A∩B) P(A and B) The rule of multiplication applies to the situation when we want to know the probability of the intersection of two events; that is, we want to know the probability that two events (Event A and Event B) both occur.

   The probability that Events A and B both occur is equal to the probability that Event A occurs times the probability that Event B occurs, given that A has occurred. P(A and B) = P(A|B)P(A) or P(A and B) = P (B|A)P(A)

2. Probability Range

   0 ≤ P(A) ≤ 1

3. Rule of Complementary Events

   P(AC) + P(A) = 1

4. Rule of Addition P(A∪B) P(A or B) We have two events, and we want to know the probability that either event occurs.

   The probability that Event A or Event B occurs is equal to the probability that Event A occurs plus the probability that Event B occurs minus the probability that both Events A and B occur. P(A∪B) = P(A) + P(B) - P(A∩B) Invoking the fact that P(A ∩ B) = P( A )P( B | A ), the Addition Rule can also be expressed as P(A ∪ B) = P(A) + P(B) - P(A)P( B | A )

5. Conditional Probability

   P(A | B) = P(A∩B) / P(B)

6. Bayes Formula

   P(A | B) = P(B | A) ⋅ P(A) / P(B)

7. Independent Events

   Events A and B are independent iff P(A∩B) = P(A) ⋅ P(B)

8. Chain rule

9. Kolmogorovs Axions

   0 ≤ P(A) ≤ 1 P(true) = 1 P(false = 0) P(a ∨ b) = P(a) + P(b) − P(a ∧ b)

10. Bayes rule in distribution form

    αP(X|Y )P(Y )

11. How can P(B) be calculated if we're not given it?

    P(B|A)P(A) + P(B|not A)P(not A) or P(B and A) + P(B and not A)