1. Introductory Statistics
Lesson 3.1 A
Objective: SSBAT identify sample space and find probability of simple events.
Standards: M11.E.3.1.1

2. Probability
 Measures how likely it is for something to occur
 A number between 0 and 1
 Can be written as a fraction, decimal or percent
Probability equal to 0  Impossible to happen
Probability equal to 1  Will definitely occur

3. Probability is used all around us and can be used to help make decisions.
 Weather
“There is a 90% chance it will rain tomorrow.”
You can use this to decide whether to plan a trip to the amusement park tomorrow or not.
Surgeons
“There is a 35% chance for a successful surgery.”
They use this to decide if you should proceed with the surgery.

4. Probability Experiment
An action, or trial, through which specific results (counts, measurements, or responses) are obtained.

5. Outcome
The result of a single trial in an experiment
Example: Rolling a 2 on a die

6. Sample Space
The set of ALL possible outcomes of a probability experiment.
Example: Experiment  Rolling a Die
Sample Space: 1, 2, 3, 4, 5, 6

7. Event
A subset (part) of the sample space.
It consists of 1 or more outcomes
 Represented by capital letters
Example: Experiment  Rolling a Die
Event A: Rolling an Even Number

8. A method to list all possible outcomes
Teacher
Tree Diagram
A method to list all possible outcomes

9. Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
A probability experiment that consists of Tossing a Coin and Rolling a six-sided die.
a) Make a tree diagram

10. Sample Space: {H1, H2, H3, H4, H5, H6,T1, T2, T3, T4, T5, T6}
Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
A probability experiment that consists of Tossing a Coin and Rolling a six-sided die.
a) Make a tree diagram
H T
Sample Space: {H1, H2, H3, H4, H5, H6,T1, T2,
T3, T4, T5, T6}

11. Examples: Find each for all of the following
a) Identify the Sample Space
b) Determine the number of outcomes
A probability experiment that consists of Tossing a Coin and Rolling a six-sided die.
b) There are 12 outcomes

12. An experimental probability that consists of a person’s response to the question below and that person’s gender.
Survey Question: There should be a limit on the number of terms a U.S. senator can serve.
Response Choices: Agree, Disagree, No Opinion a)
Sample Space: {FA, FD, F NO, MA, MD, M NO}
b) There are 6 outcomes

13. A probability experiment that consists of tossing a coin 3 times.
Teacher
A probability experiment that consists of tossing a coin 3 times. a)
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTH, TTT}
b) There are 8 outcomes

14. Fundamental Counting Principle
A way to find the total number of outcomes there are
It does not list all of the possible outcomes – it just tells you how many there are
If one event can occur in m ways and a second event can occur n ways, the total number of ways the two events can occur in sequence is m·n
 This can be extended for any number of events

15. In other words:
The number of ways that events can occur in sequence is found by multiplying the number of ways each event can occur by each other.

16. Take a look at a previous example and solve using the Fundamental Counting Principle.
How many outcomes are there for Tossing a Coin and Rolling a six sided die?
There are 2 outcomes for the coin
There are 6 outcomes for the die
 Multiply 2 times 6 together to get the total number of outcomes
Therefore there are 12 total outcomes.

17. You are purchasing a new car
You are purchasing a new car. The possible manufacturers, car sizes, and colors are listed below. How many different ways can you select one manufacturer, one car size, and one color?
Manufacturer: Ford, GM, Honda
Car Size: Compact, Midsize
Color: White, Red, Black, Green
 · 2 · 4 = 24
There are 24 possible combinations.

18. There are 10,000 possible access codes.
The access code for a car’s security system consists of four digits. Each digit can be 0 through 9 and the numbers can be repeated.
 there are 10 possibilities for each digit
 10 · 10 · 10 · 10 = 10,000
There are 10,000 possible access codes.

19. There are 5,040 possible access codes.
The access code for a car’s security system consists of four digits. Each digit can be 0 through 9 and the numbers cannot be repeated.
 There are 10 possibilities for the 1st number and then subtract 1 for the next amount and so on
 10 · 9 · 8 · 7 =
There are 5,040 possible access codes.

20. How many 5 digit license plates can you make if the first three digits are letters (which can be repeated) and the last 2 digits are numbers from 0 to 9, which can be repeated?
 there are 26 possible letters and 10 possible numbers
26 · 26 · 26 · 10 · = 1,757,600
There are 1,757,600 possible license plates

21. 5. How many 5 digit license plates can you make if the
5. How many 5 digit license plates can you make if the first three digits are letters, which cannot be repeated, and the last 2 digits are numbers from 0 to 9, which cannot be repeated?
26 · 25 · 24 · 10 · 9 = 1,404,000
There are 1,404,000 possible license plates

22. How many ways can 5 pictures be lined up on a wall?
5 · 4 · 3 · 2 · 1
There are 120 different ways.

23. Simple Event
An event that consists of a single outcome
Example of a Simple Event
Rolling a 5 on a die - There is only 1 outcome, {5}
Example of a Non Simple Event
 Rolling an Odd number on a die – There are 3 possible outcomes: {1, 3, 5}

24. Experiment: Rolling a 6 sided die
Determine the number of outcomes in each event.
Then decide whether each event is simple or not?
Experiment: Rolling a 6 sided die
Event: Rolling a number that is at least a 4
 There are 3 outcomes (4, 5, or 6)
 Therefore it is not a simple event

25. 2. Experiment: Rolling 2 dice Event: Getting a sum of two
Determine the number of outcomes in each event.
Then decide whether each event is simple or not?
2. Experiment: Rolling 2 dice
Event: Getting a sum of two
 There is 1 outcome (getting a 1 on each die)
 Therefore it is a simple event

26. Complete Page 142 #1, 2, 3, 5 – 16, 36A, 37 – 41