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5.1 Introducing Probability
Objectives:
By the end of this section, I will be
able to…
1)
2)
3)
Understand the meaning of an experiment,
an outcome, an event, and a sample space.
Describe the classical method of assigning
probability.
Explain the Law of Large Numbers and the
relative frequency method of assigning
probability.
Rules of Probability
1.
2.
Probabilities must be
between 0 and 1.
For any experiment, the
sum of all outcome
probabilities must = 1
Probability terms
Outcome:
result of
experiment.
Sample Space: all the
possible outcomes of
experiment
PROBABILITY
number of favorable outcomes
𝑝(𝐴) =
TOTAL number of outcomes
number of favorable outcomes
𝑝(𝐴) =
sample space
Experimental Probability vs.
Theoretical Probability
 Roll
ONE die 15 times.
 WRITE
 What
OUT your results.
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
__
= 1 ways
6
TWO DICE
 Two
dice are rolled at the same time.
Find the sample space.
1,1
2,1
3,1
4,1
5,1
6,1
1,2
2,2
3,2
4,2
5,2
6,2
1,3
2,3
3,3
4,3
5,3
6,3
1,4
2,4
3,4
4,4
5,4
6,4
1,5
2,5
3,5
4,5
5,5
6,5
1,6
2,6
3,6
4,6
5,6
6,6
36
TWO DICE
4)
With two dice, what is the probability that
you will roll a seven?
6,1 1,6 2,5
5)
5,2
4,3 3,4 = 6 ways
With two dice, what
is the probability that
6
__
you will roll a number larger than 10?
5,6
11
6,5
6,6
12
36 = 3 ways
3
__
36
DECK OF CARDS




52
How many cards are in a deck?
How many face cards are there? 12
How many suits are in a deck of cards? 4
How many cards are in each suit? 13
DECK OF CARDS
What is the probability of getting…

A face card?
12 = # of face cards
52 = sample space

A red two?
2
__
52
= # of red twos
= sample space
Tree Diagrams
 Draw
a Tree Diagram to represent what
can happen when you toss a coin.
Tree Diagrams
1
2
Toss a
Coin
1
2
H
1
2
H
1
2
T
1
2
T
1
2
H
T
P(H) = 1/2
P(H,H) =
½·½=¼
Use the following table to find the probability
 Find
the probability that a randomly selected
worker at McDonalds
2) Is a college grad 63 / 169
3) Is a male 78 / 169
31 / 169
4) Is a male who graduated from Grad school
HS
College
Graduate
MALES
20
27
27
31
31
FEMALES
26
36
29
63
78
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?