Slide Slide 1 Survey 1)Locate the following countries on your map: Venezuela, Hungary, Syria, Vietnam, North Korea, Egypt, Pakistan, Guatemala, Germany, Israel 2) Do you read novels or poems for pleasure? (Yes/No) 3) Over the past year, how many books did you read for pleasure (not for school)? (Estimate) 3) Do you think its necessary to know the location of other countries in which important news is being made?

Slide Slide 2 Warm Up (Easy!) A medical center has 18 female physicians and 2 male physicians. a)If a patient randomly selects one of the physicians, what is the probability of getting a male? b)Is it unusual for a patient to get a male when a physician is randomly selected? Why or why not?

Slide Slide 3 Section 4-3 Addition Rule

Slide Slide 4 Key Concept The main objective of this section is to present the addition rule as a device for finding probabilities that can be expressed as P(A or B), the probability that either event A occurs or event B occurs (or they both occur) as the single outcome of the procedure.

Slide Slide 5 Compound Event any event combining 2 or more simple events Definition Notation P(A or B) = P (in a single trial, event A occurs or event B occurs or they both occur)

Slide Slide 6 When finding the probability that event A occurs or event B occurs, find the total number of ways A can occur and the number of ways B can occur, but find the total in such a way that no outcome is counted more than once. General Rule for a Compound Event

Slide Slide 7 Compound Event Intuitive Addition Rule To find P(A or B), find the sum of the number of ways event A can occur and the number of ways event B can occur, adding in such a way that every outcome is counted only once. P(A or B) is equal to that sum, divided by the total number of outcomes in the sample space. Formal Addition Rule P(A or B) = P(A) + P(B) – P(A and B) where P(A and B) denotes the probability that A and B both occur at the same time as an outcome in a trial or procedure.

Slide Slide 8 Example Assuming that 1 person is randomly selected from the 300 people that were tested, find the probability of selecting a subject who had a positive test result or used marijuana. Did the Subject Actually Use Marijuana? YESNO TOTAL Positive test result 119 (true positive) 24 (false positive) 143 Negative test result 3 (false negative)154 (true negative) 157 Total

Slide Slide 9 Example Considerable controversy arose when New York City introduced a program of keeping the cars belonging to people charged with drunk driving. The Associated Press conducted a poll, and the table below is based on the results. If one of the respondents is randomly selected, find the probability of getting a man or someone who answered yes. Should car be seized? YESNOTOTAL MEN WOMEN TOTAL

Slide Slide 10 Definition Events A and B are disjoint (or mutually exclusive) if they cannot occur at the same time. (That is, disjoint events do not overlap.) Venn Diagram for Events That Are Not Disjoint Venn Diagram for Disjoint Events

Slide Slide 11 Complementary Events P(A) and P(A) are disjoint It is impossible for an event and its complement to occur at the same time.

Slide Slide 12 Rules of Complementary Events P(A) + P(A) = 1 = 1 – P(A) P(A) = 1 – P(A) P(A)

Slide Slide 13 Venn Diagram for the Complement of Event A

Slide Slide 14 Example 1) Determine whether the following events are disjoint: A: Getting a subject with a negative test result; B: getting a subject who did not use marijuana. 2) Assuming that 1 person is randomly selected from the 300 people that were tested, find the probability of selecting a subject who had a negative test result or did not use marijuana. Did the Subject Actually Use Marijuana? YES NO TOTAL Positive test result 119 (true positive) 24 (false positive) 143 Negative test result 3 (false negative) 154 (true negative) 157 Total

Slide Slide 15 Recap In this section we have discussed:  Compound events.  Formal addition rule.  Intuitive addition rule.  Disjoint events.  Complementary events.