1. Lecture PowerPoint Slides Basic Practice of Statistics 7 th Edition

2. In chapter 13, we cover … The general addition rule The multiplication rule Conditional probability The general multiplication rule

3. Everything in this chapter follows from the four rules we learned in Chapter 12: Probability rules Rule 1. For any event A, 0 ≤ P(A) ≤ 1. Rule 2. If S is the sample space, P(S) = 1. Rule 3. Addition rule: If A and B are disjoint events, P(A or B) = P(A) + P(B). Rule 4. For any event A, P(A does not occur) = 1 – P(A). Rule 1. For any event A, 0 ≤ P(A) ≤ 1. Rule 2. If S is the sample space, P(S) = 1. Rule 3. Addition rule: If A and B are disjoint events, P(A or B) = P(A) + P(B). Rule 4. For any event A, P(A does not occur) = 1 – P(A).

4. Venn diagrams Sometimes it is helpful to draw a picture to display relations among several events. A picture that shows the sample space S as a rectangular area and events as areas within S is called a Venn diagram.

5. The general addition rule  We know if A and B are disjoint events, P(A or B) = P(A) + P(B) Addition Rule for Any Two Events  For any two events A and B: P(A or B) = P(A) + P(B) – P(A and B)

6. Multiplication rule for independent events If two events A and B do not influence each other; that is, if one event will happen is not influenced by whether or not a second event happens; then the events are said to be independent of each other. MULTIPLICATION RULE FOR INDEPENDENT EVENTS If A and B are independent: The probability that both events will occur is the product of their separate probabilities. P(A and B) = P(A)  P(B)

7. Conditional probability

8. Conditional probability Rule  Instead of the entire sample space S, we now have a sample space of A since we know A has occurred  It is the number in A and B divided by the number in A (must be in A since A has occurred). then you have the probability of A and B divided by the probability of A

9. Example of P(B|A) Problem: A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test? P(Second | First) = P(First and Second) / P(First) = 0.25/0.42 = 0.60 = 60 %

10. The general multiplication rule,