Probability Models Vocabulary Terms Mutually Exclusive/Disjoint General Addition Rule

Probability Terminology Refer to Section 5.2 Notes Sample Space – List of all possible outcomes of a random event. Flip a coin S = {H, T}; if you survey 1000 adults about their approval of the President, then the S = {Combination of all poss. Outcomes} Event – Subset of a sample space. Typically labeled by capital letters. For Example, you could let A = Flip H or B = Roll a “7” with a pair of dice The symbol for “The probability of event A” = P(A)

Basic Probability Rules The probability of any event A satisfied 0 < P(A) < 1 If S is the sample space, P(S) = 1 The complement of event A, labeled A c, is that event A does not occur. P(A) + P(A c ) = 1 The complement Rule: P(A c ) = 1 – P(A) Events A and B are mutually exclusive/disjoint if and only iff events A and B cannot occur at the same time. If mutually exclusive/disjoint P(A and B) = 0

Addition Rule for Mutually Exclusive/Disjoint Events If events A and B are mutually exclusive, then……… P(A or B) = P(A) + P(B) Given the following distribution of colors of M&M Peanut: Color: Brown Red Yellow Green Orange Blue Prob: ? Find P(Blue) Find P(Brown or Blue) Find P(Not Red)

Problem Solving & Probability Calculation Take a Standard Deck of 52 playing cards Let A – Card selected is a heart Let B – Card selected is a face card (J,Q,K) Find P(A) Find P(B) Find P(A or B)

General Addition Rule Let A = Get an A in AP Stats, P(A) =.15 Let B = Get a B in AP Stats, P(B) =.30 Find P(A orB) Let C = Get an A in Religion, P(C) =.40 Find P(A or C) Set up a 2-way table Set up a Venn Diagram

General Addition Rule P(A or B) = P(A) + P(B) – P(A and B) Note: if A and B are mutually exclusive/disjoint, then P(A and B) = 0 (end up with special case) Let A = Has Blue Eyes, P(A) =.20 Let B = Has Blonde Hair P(B) =.30 P(A and B) =.18 P(A or B) =

Problem Solving Strategies Reminder: A = Blue eyes, P(A) =.20 and B = Blonde Hair, P(B) =.30 and P(A and B) =.18 Probability an individual has blue eyes but does not have blonde hair? P(A and B c ) Probability an individual does not have either blue eyes nor blonde hair? P(A c and B c ) Set up Venn Diagram Set up a two-way table

Example Likes Gospel Music Doesn’t Like Gospel Music Total Likes Country Music Does Not Like Country Music Total Find probability of liking Gospel Music? 2.Find probability of liking Country Music? 3.Find probability of liking Gospel and County? 4.Find probability of liking Gospel or Country? 5.Find probability of liking Gospel given you like Country?

Examples Zach has applied to both Princeton and Stanford. He thinks his probability of getting into Princeton is.4 and his probability of getting into Stanford is.5. Furthermore, he feels like his probability of getting into both schools is.25. Find probability of getting into at least one school? Find probability of getting into Stanford but not into Princeton? Find the probability of getting rejected at both?