5.1 Introducing Probability Objectives: By the end of this section, I will be able to… 1) Understand the meaning of an experiment, an outcome, an event,

5.1 Introducing Probability

Objectives:By the end of this section, I will beable to…

1) Understand the meaning of an experiment, an outcome, an event, and a sample space.

2) Describe the classical method of assigning probability.

3) Explain the Law of Large Numbers and the relative frequency method of assigning probability.

Rules of Probability

1. Probabilities must be between 0 and 1.

2. For any experiment, the sum of all outcome probabilities must = 1

Probability termsOutcome: result of experiment.

Sample Space: all the possible outcomes of experiment

PROBABILITY

𝑝 (𝐴)=number  of   favorable   outcomessample   space

𝑝 (𝐴)=number  of   favorable   outcomesTOTAL  number  of  outcomes

Experimental Probability vs. Theoretical Probability

Roll ONE die 15 times.

WRITE OUT your results.

What is your probability of rolling a FIVE?

This is an example of experimental probability.

ONE DIE

THEORETICAL PROBABILITY

1) What is the probability that

you will roll a 5?

5 = 1 ways__1

6

TWO DICETwo dice are rolled at the same time.

Find the sample space.

1,1

1,2

1,3

1,4

1,5

1,6

2,1

2,2

2,3

2,4

2,5

2,6

3,1

3,2

3,3

3,4

3,5

3,6

4,1

4,2

4,3

4,4

4,5

4,6

5,1

5,2

5,3

5,4

5,5

5,6

6,1

6,2

6,3

6,4

6,5

6,6

361,2

2,1

__

TWO DICE

4) With two dice, what is the probability that you will roll a seven?

5) With two dice, what is the probability that you will roll a number larger than 10?

= 6 ways1,6 5,22,56,1 4,3 3,4

6

365,6

6,511

6,6 = 3 ways __3

3612

DECK OF CARDS How many cards are in a deck? How many face cards are there? How many suits are in a deck of cards? How many cards are in each suit?

52

124

13

__

DECK OF CARDSWhat is the probability of getting…

A face card?

A red two?

12 = # of face cards

52 = sample space

2 = # of red twos

52 = sample space

Tree Diagrams

Draw a Tree Diagram to represent what can happen when you toss a coin.

Tree Diagrams

1

2

1

2

1

2

Toss a Coin

H

TH

T

H

T

P(H) = P(H) = 1/2

P(H,H) = P(H,H) = ½ · ½ = ¼

1

2

1

2

1

2

Use the following table to find the probability

Find the probability that a randomly selected worker at McDonalds2) Is a college grad3) Is a male4) Is a male who graduated from Grad school

HS College Graduate

MALES 20 27 31

FEMALES 26 36 29

27

36

63 169

63 / 169

20 31 7827

78 / 169

31

31 / 169

Scenarios

A slot machine in VEGAS has three wheels, and each wheel has a picture of a lemon, cherry, and an apple on it. Each wheel operates independently of the other. When all three wheels show the same item, then the player wins $5000. Find the probability of a player winning $5000

when playing this slot machine.

Forgetful Students

Sallies students are very forgetful. Three of Mrs. Godfrey’s seniors left their calculators in her classroom. They all stop by after school at different times and randomly select a calculator. The calculators all look exactly the same too! What is the probability that they pick the correct one?