Independence (How Do You Prove Events Are Independent?)

AP Stats Name______Chapter 15

Vocabulary Sample Space

Disjoint events

Addition rule Disjoint:

General:

Conditional Probability

Independence (How do you prove events are independent?)

Multiplication Rule Independent:

General:

Tree Diagram

Example: Traffic Stops Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests. What is the probability that a randomly selected DWI suspect is given: a. A test? b. A blood test or a breath test, but not both? c. Neither test?

Example: Girls and Sports In a recent study it was found that the probability that a randomly selected student is a girl is .51 and is a girl and plays sports is .10. If the student is female, what is the probability that she plays sports?

Example 3: Boys and Sports The probability that a randomly selected student plays sports if they are male is .31. What is the probability that the student is male and plays sports if the probability that they are male is .49? Example: Probabilities from two way tables

Stu Staff Total American 107 105 212 European 33 12 45 Asian 55 47 102

1. WhatTotal is the probability195 that the driver164 is a student?359

2. What is the probability that the driver drives a European car?

3. What is the probability that the driver drives an American or Asian car?

4. What is the probability that the driver is staff or drives an Asian car?

5. What is the probability that the driver is staff and drives an Asian car?

6. If the driver is a student, what is the probability that they drive an American car?

7. What is the probability that the driver is a student if the driver drives a European car?

Example: Conditional Probability At George Washing HS, after school activities can be classified into three types: athletic, fine arts, and other. The following table gives the number of students participating in these types of activities by grade: 9th 10th 11th 12th Total Athletics 150 160 140 150 600 Fine Arts 100 90 120 125 435 Other 125 140 150 150 565 Total 375 390 410 425 1600

Is it true from the table that:  There are 160 10th graders participating in athletic?  The number of senior participating in fine arts activities is 125?  There are 435 students in fine arts activities?  GWHS has 410 juniors?  The total number of students is 1600?

What is the probability that a randomly selected student is a senior athlete?

What is the probability that the selected student is an athlete, given that the student is a senior?

Example: GFI Switches A GFI (ground fault interrupt) switch turns off power to a system in the event of an electrical malfunction. A spa manufacturer currently has 25 spas in stock, each equipped with a single GFI sw9itch. Two different companies supply the switches and some of the switches are defected as summarized in the table: Nondefective Defective Total Company 1 10 5 15 Company 2 8 2 10 Total 18 7

Find: P(E) P(D) P(E and D) = P(E∩D) Now suppose that testing reveals a defective switch. How likely is it that the switch came from the first company?

Example: Management has determined that customers return 12% of the items assembled by inexperienced employees, whereas only 3% of the items assembled by experienced employees are returned. Due to turnover and absenteeism at an assembly plant, inexperienced employees assemble 20% of the items. Construct a tree diagram or a chart for this data.

What is the probability that an item is returned?

If an item is returned, what is the probability that an inexperienced employee assembled it?