AP Statistics
Chapter 15
Objectives: At the end of this chapter you should be able to:
 Understand conditional probability.
 Understand independence.
 Understand and apply the General Addition Rule & General Multiplication Rule.
 Know how to find probabilities for compound events.
 Know how to make and use a tree diagram.
______________________________________________________________________________
Sample space: the ____________________ of all possible ____________________.
Notation:
Example:
Probability: P(A) = count of outcomes in A
Count of all possible outcomes
General Addition Rule: the _________ of the probabilities of two events, ________ the
probability of their _________________.
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
Venn Diagram:
Example: When taking a sample of the pages in your textbook we find the following:
48% of pages had some kind of data display
27% of pages had an equation, and
7% of pages had both a data display and an equation
a) Display these results in a Venn diagram
b) What is the probability that a randomly selected sample page had neither a data
display nor an equation.
c) What is the probability that a randomly selected sample page had a data display but
no equation.
Example: 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?
Conditional Probability: the _______________ of an event from a _______________________
𝑃(𝐵|𝐴) =
𝑃(𝐴∩𝐵)
𝑃(𝐴)
General Multiplication Rule: does not require ______________________
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐴) × 𝑃(𝐵|𝐴)
It is also true that
𝑃(𝐴 ∩ 𝐵) = 𝑃(𝐵) × 𝑃(𝐴|𝐵)
Independence: if events A and B are ___________________, then
P(B|A) = P(B)
Example: Going back to our previous example where:
48% of pages had a data display
27% of pages had an equation
7% of pages had both a data display and an equation
Display
a) Make a contingency table for the variables display and equation
Equation
Yes
No
Total
Yes
No
Total
b) What is the probability that a randomly selected sample page with an equation also
had a data display?
c)
Are having an equation and having a data display disjoint events?
d) Are having an equation and having a data display independent events?
Drawing without Replacement:
Example: Suppose you have 10 bills in a bag, 5 are $1 bills, and 5 are $10 bills. You get to draw 2
bills out of the bag. What are the chances that you will draw 2 $10 bills?
Tree Diagrams: used to display _______________events or _________________. Can be
helpful when thinking through conditioning or when you will be using the general multiplication
rule.
Example: According to a study by the Harvard School of Public Health, 44% of college students
engage in binge drinking, 37% drink moderately, and 19% abstain entirely. Another study,
published in the American Journal of Health Behavior, finds that among binge drinkers aged 21
to 34, 17% have been involved in an alcohol-related automobile accident, while among
nonbingers of the same age, only 9% have been involved in such accidents.
See tree diagram on page 356
Reversing the Conditioning:
If a student has a alcohol-related accident, what’s the probability that the student is a binge
drinker?
HW: Read Chapter 15
Problems: p.362(1 – 9 odd, 15, 19, 21, 25, 29, 31, 45)