Chapter 15 Probability Rules Ryan Vu and Erick

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

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

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

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

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