Transcript 5.2 Part 2

Warm up!
Put these on a separate sheet of paper. I might
RANDOMLY decide to collect!
Determine a method to simulate each of the following
events:
 If 15% of all AP statistics students get a “5” on the AP
exam, how many would we need to randomly select
until we selected someone who got a “5”?
 A professional basketball player has a 73% free throw
percentage, and needs to make their next two free
throw attempts.
Homework questions
5.2
Venn Diagrams
Issue from yesterday…
 When we find P(A or B) we were having to add up
individual cells from our tables.
 When we say we are going to the football game or
watching a movie that usually means we will do one or the
other, BUT NOT BOTH!
 In statistics, “A or B” could mean one or the other or
both…
 When we did those problems in yesterday’s notes we
added each cell and divided by the total to get P(A or B)
Another way to look at it
 Find P(male or pierced ears)
Gender
Yes
No
Total
Male
19
71
90
Female
84
4
88
Total
103
75
178
Venn Diagrams
 P(A) = 90/178
 P(B) = 103/178
 P(A and B) = 19/178
 The middle is double counted if we
simply add
 P(A or B) = P(A) + P(B) – P(A and B)
General Addition Rule for Two Events
 P(A or B) = P(A) + P(B) – P(A and B)
 If the events happen to be mutually exclusive…
Compliment
Mutually Exclusive or Disjoint
A and B
𝐴∩𝐵
A or B
𝐴∪𝐵
Example
 In an apartment complex, 40% of residents read USA Today.
Only 25% read the New York Times. Five percent of residents
read both papers. Suppose we select a resident of the
apartment complex at random and record which of the
following two papers the person reads.
 Made a two-way table (assume 100 people total to make easy)
 Construct a Venn Diagram
 Find the probability that the person reads at least one of the two
papers.
 Find the probability that the person doesn’t read either paper.
Two-Way Table
Reads New York
Times
Yes
No
Total
Yes
5
20
25
No
35
40
75
Total
40
60
100
Venn Diagram
Answer Questions
 C)
𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 ∩ 𝐵)
 D) 𝑃 𝐴𝐶 ∩ 𝐵𝐶 =
 (or the compliment of reads at least one paper)
Homework
 Section 5.2 homework: Pg. 309 (3946, 49-56)