School

Collin County Community College District **We aren't endorsed by this school

Course

MATH 1342

Subject

Statistics

Date

Aug 29, 2023

Pages

28

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Chapter 5 Probability
5.1 Probability Terminology and Notation
Basic Definitions
When discussing probability, an
experiment
is any process with uncertain results that can be
repeated many times. Common probability experiments include:
Tossing a coin
Rolling a die
Drawing a card from a deck
Randomly selecting a sample from a population
When an experiment is repeated multiple times, each repetition is called a
trial
A possible result of the experiment is called an
outcome
The
sample space
is the set of all possible outcomes.
Tossing a Coin:
Heads, Tails
Rolling a Die:
1, 2, 3, 4, 5, 6
Drawing a Card:
A ♠ ,
2
♠ ,
3
♠,
4
♠ ,
5
♠ ,
6
♠ ,
7
♠,
8
♠ ,
9
♠ ,
10
♠ ,J ♠,Q♠ ,K ♠ ,
A
♡
,
2
♡
,
3
♡
,
4
♡
,
5
♡
,
6
♡
,
7
♡
,
8
♡
,
9
♡
,
10
♡
,J
♡
,Q
♡
,K
♡
,
A
♢
,
2
♢
,
3
♢
,
4
♢
,
5
♢
,
6
♢
,
7
♢
,
8
♢
,
9
♢
,
10
♢
,J
♢
,Q
♢
,K
♢
,
A ♣ ,
2
♣ ,
3
♣,
4
♣ ,
5
♣ ,
6
♣ ,
7
♣,
8
♣ ,
9
♣ ,
10
♣ ,J ♣,Q♣ ,K ♣
A collection of outcomes is called an
event
Events can be described in words or by listing their
outcomes.
Example.
Suppose a standard die is rolled. List all the possible ways of rolling an odd number.
1, 3, 5
Example.
Suppose a coin is tossed three times. List all the possible ways of getting at least two
heads.
H H H
H T H
H H
T
T H H
1

Example.
Suppose two dice are rolled. List all the possible ways for the sum to be 8.
6+2, 5+3, 4+4, 3+5, 2+6
Example.
Suppose two dice are rolled. List all the possible ways of rolling doubles.
1+1, 2+2, 3+3, 4+4, 5+5, 6+6
Is it possible to roll doubles and for the sum to be 8?
4+4
Is it possible to roll doubles and for the sum to be 7?
No
Two events are
mutually exclusive
(or
disjoint
) if they have no outcomes in common. Hence it is
impossible for both events to occur on the same trial of the experiment.
Example.
A card is drawn from a standard deck. Which of the following events are mutually
exclusive?
Drawing an eight
Drawing a heart
Drawing a spade
Drawing a face card
Drawing an eight and a face card = mutually exclusive
Drawing a heart and spade = mutually exclusive
2

If
A
and
B
are mutually exclusive events, knowing that
A
has occurred makes it less likely that
B
has also occurred. (In fact, it makes it impossible for
B
to occur.) Similarly, knowing that
B
has
occurred makes it less likely for
A
to occur.
Two events are
dependent
if knowing that one of the events has occurred makes it more or less
likely that the other event has occurred. Two events are
independent
if neither event affects
the likelihood of the other.
Example.
A coin is tossed twice. Event
A
is getting heads on the first toss. Event
B
is getting
heads on the second toss. Are
A
and
B
independent?
Independent
Example.
Two dice are rolled. Event
A
is the sum being greater than 10. Event
B
is rolling a six on
the first die. Are these events independent?
No, they're dependent
Example.
A student is selected at random. Event
A
occurs if the student is taller than 72 inches.
Event
B
occurs if the student's shoe size is greater than 10. Are these events dependent?
Yes
Example.
A student is selected at random. Event
A
occurs if the student got more than 7 hours
of sleep the night before. Event
B
occurs if the student's shoe size is greater than 10. Are these
events dependent?
No, they're independent
3

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