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Addition & Multiplication Rules

Addition & Multiplication Rules. BUSA 2100, Section 4.3. Special Addition Rule. Example 1 : In Lowndes County, 25% of the cars owned were made by GM and 20% were made by Ford. What is the probability that a randomly chosen car was made by GM or Ford?. Special Addition Rule, p. 2 .

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Addition & Multiplication Rules

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  1. Addition & Multiplication Rules BUSA 2100, Section 4.3

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

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

  4. General Addition Rule • Ex. 2: Among junior VSU Business majors, 35% are taking BUSA 2100 this term, and 45% are taking MGNT 3250. • What is the probability that a junior Business student is taking Statistics or Management? • Can we just add the probabilities? Draw a Venn diagram.

  5. General Addition Rule, Page 2 • If in doubt, use the GeneralAdd. Rule.

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

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

  8. Independent and Dependent Events, Page 3 • Example 2: C = “man with a shoe size > 10”; D = “man with IQ > 115”. Are C, D independent or dependent? Why? • 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?

  9. Special Multiplication Rule

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

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