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Section 11.4 Addition and Complement Rule

Section 11.4 Addition and Complement Rule. Definition of Addition Rule (Page 731). Addition Rule for Probabilities with Mutually Exclusive Events: Two events A and B are mutually exclusive if they cannot occur at the same time, i.e., the intersection of A and B is empty.

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Section 11.4 Addition and Complement Rule

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  1. Section 11.4Addition and Complement Rule

  2. Definition of Addition Rule (Page 731) • Addition Rule for Probabilities with Mutually Exclusive Events: Two events A and B are mutually exclusive if they cannot occur at the same time, i.e., the intersection of A and B is empty. • Probability of Mutually Exclusive Events: If A and B are mutually exclusive, then P(A U B) = P(A) + P(B)

  3. Example for Addition Rule • Example Two fair dice are tossed once. What is the probability of rolling a 7 or 11? (page 732)

  4. Addition Rule for Probabilities • Addition Rule for Probabilities P(A or B) = P(A) + P(B) - P(A and B) • Example (example 2 on page 733) The table shows data from an experiment. If one person is selected from population, what is the probability that the person was vaccinated or contracted the flu?

  5. Complement of an Events • The complement of an event E is the subset of outcomes not in E, denoted by E′. • Probability of the Complement of E: P(E′) = 1 - P(E) • Example The probability of tossing a sum of 11 on the toss of two dice is 1/18. What is the probability of not tossing a sum of 11 on the toss of two dice?

  6. Example of Complement of an Event • Example Suppose that there are 40 dinner plates, of which 3 are defective. If 5 plates are randomly selected from the 40, what is the probability that at least one is defective? (Page 736-737)

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