1. AP Review Day 2: Discrete Probability

2. Basic Probability Sample space = all possible outcomes P(A c ) = 1 – P(A) Probabilities have to be between 0 and 1 Sum of all possibilities has to = 1

3. AND/OR AND: – If A and B are independent, then P(A and B) = P(A) · P(B) – If A and B are not independent, use the General Multiplication Rule: P(A and B) = P(A) · P(B|A) Conditional Probability: – P(B|A) = the probability of B given A

4. AND/OR OR: – If A and B are disjoint(mutually exclusive), then P(A or B) = P(A) + P(B) – If A and B overlap, use the General Addition Rule: P(A or B) = P(A) + P(B) – P(A∩B) Disjoint/Mutually ExclusiveNon-Disjoint/Not Mutually Exclusive

5. From a Table P(Liberal) = P(Male) = P(Liberal|Male) = LiberalModerateConservativeTotal Male19392482 Female23281263 Total426736145

6. Independence If two events are independent, then In other words, knowing A is true doesn’t change the probability of B Since P(Liberal) ≠ P(Liberal|Male), gender and political identification are not independent

7. Probability Distributions Has to add up to 1 These formulas are on your formula sheet Don’t forget X012345 P(X).21.29.34.05.01

8. Combining Distributions For means, just do whatever you do to the variables: For standard deviations, use these rules:

9. Binomial Requirements: 1)2 possible outcomes (success/failure) 2)Fixed number of trials (n) 3)Each trial is independent 4)Probability of success (p) stays the same for each trial DISTR menu on calculator (write binomial, with n= and p=)