1. Chapter 15: Probability Rules! Ryan Vu and Erick Li Period 2

2. Terms ●Sample Space The collection of all possible outcome values. The sample space has a probability of 1. ●Disjoint events Two events are disjoint (or mutually exclusive) if they have no outcomes in common. ●Addition Rule If A and B are disjoint events, then the probability of A or B is P(A ∪ B) = P(A) + P(B). ●General Addition Rule For any two events, A and B, the probability of A or B is P(A ∪ B) = P(A) + P(B) - P(A∩B). ●Conditional probability P(B|A) = P(A∩B) / P(A) ;P(B|A) is read “the probability of B given A.” ●Independence (used casually) Two events are independent if knowing whether one event occurs does not alter the probability that the other event occurs.

3. Terms ●Multiplication Rule If A and B are independent events, then the probability of A and B is P(A∩B) = P(A) × P(B). ●General Multiplication Rule For any two events, A and B is P(A∩B) = P(A) × P(B|A). ●Independence (used formally) Events A and B are independent when P(B|A) = P(B). ●Tree diagram A display of conditional events or probabilities that is helpful in thinking through conditioning

4. Problem 11; Page 363 a) P(P∩C) =.11 b) P(P) =.11 +.16 =.27 c) P(C|P) = P(C∩P) / P(P) =.11 / (.11 +.16) =.4074 d) P(P|C) = P(P∩C) / P(C) =.11 / (.11 +.21) =.3438

5. Problem 13; Page 364 a) P(18∩C) = outcome(18∩C) / outcome(all) = 135 / 1005 =.1343 b) P(C|18) = outcome(C∩18) / outcome(18) = 135 / 217 =.6221 c) P(18|C) = outcome(18∩C) / outcome(C) = 135 / 437 =.3089 d) P(65|B) = outcome(65∩B) / outcome(B) = 92 / 518 =.1776

6. Problem 13; Page 364 e) P(B|65) = outcome(B∩65) / outcome(65) = 92 / 167 =.5509