Addition & Multiplication Rules BUSA 2100, Section 4.3

Special Addition Rule l Example 1: In Lowndes County, 25% of the cars owned were made by GM and 20% were made by Ford. l What is the probability that a randomly chosen car was made by GM or Ford?

Special Addition Rule, p. 2 l Draw a Venn diagram for Example 1. l Can be extended to more than 2 events.

General Addition Rule l Ex. 2: Among junior VSU Business majors, 35% are taking BUSA 2100 this term, and 45% are taking MGNT l What is the probability that a junior Business student is taking Statistics or Management? l Can we just add the probabilities? Draw a Venn diagram.

General Addition Rule, Page 2 l If in doubt, use the General Add. Rule.

Independent and Dependent Events l Definition: Two events are independent if the occurrence of one event has no effect on whether or not the other event occurs. l Two events are dependent if the occur- rence of one event has some effect on whether or not the other event occurs.

Independent and Dependent Events, Page 2 l If 2 events are dep., it doesn’t mean 1 event causes or requires the other. l Dependence means the occurrence of 1 event affects (increases, decreases) the probability that the other will occur. l Ex. 1: A = “family with annual income > $100,000”; B = “family with luxury car < 2 years old”. Are A, B indep. or dep.?

Independent and Dependent Events, Page 3 l Example 2: C = “man with a shoe size > 10”; D = “man with IQ > 115”. Are C, D independent or dependent? Why? l Example 1: A coin is flipped and a die is rolled. What is the probability of a head on the coin and a six on the die?

Special Multiplication Rule

Special Multiplication Rule, Page 2 l Example 2: At a gas station, 70% of the customers use credit cards. l For the next 2 customers, what is the probability that the 1st one uses a credit card and the 2nd one does not?