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.

Warm up!Put these on a separate sheet of paper. I might

RANDOMLY decide to collect!

Homework questions

5.2Venn Diagrams

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)

Issue from yesterday…

Find P(male or pierced ears)

Another way to look at it

Gender Yes No Total

Male 19 71 90

Female 84 4 88

Total 103 75 178

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)

Venn Diagrams

P(A or B) = P(A) + P(B) – P(A and B)

If the events happen to be mutually exclusive…

General Addition Rule for Two Events

Compliment

Mutually Exclusive or Disjoint

A and B

A or B

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.

Example

Reads New York Times

Yes No Total

Yes 5 20 25

No 35 40 75

Total 40 60 100

Two-Way Table

Venn Diagram

C)

D)

(or the compliment of reads at least one paper)

Answer Questions

𝑃 ( 𝐴∪𝐵 )=𝑃 ( 𝐴 )+𝑃 (𝐵 )− 𝑃 (𝐴∩𝐵)

Section 5.2 homework: Pg. 309 (39-46, 49-56)

Homework