Download Probability

Unit 4
Sections 4-1 & 4-2
4-1 & 4-2: Sample Spaces and
Probability

Probability– the chance of an event occurring.

Probability event – a chance process that leads to
a well defined result (outcome).


Outcome – the result of a single trial of a
probability experiment.


Ex: rolling a die, flipping a coin
Ex: flipping heads or tails
Sample Space – the set of all possible outcomes a
probability experiment.
Section 4-2
Determining Sample Spaces

Example 1: Determine the sample space for each
probability experiment.
Experiment
Toss one coin
Roll a die
Answer a true/false
question
Toss Two Coins
Sample Space
Section 4-2
Determining Sample Space

Example 2: Determine the sample space for rolling two
dice.
1
2
3
4
5
6
1
2
3
4
5
6
Section 4-2
Determining Sample Space

Example 3: Determine the sample space for the gender
of the children if a family has three children.
(Use B for boy and G for girl)
Section 4-2

Tree Diagram – a device consisting of line segments
emanating from a starting point and also from the
outcome point.


Used to determine all possible outcomes of a probability
experiment.
Example 4: Using a tree diagram, determine the sample
space for the gender of the children if a family has three
children.
Section 4-2

Event – set of outcomes of a probability
event.
Ex: rolling and odd number
 Event with one outcome is called a simple
event.
 Event with more than one outcome is called a
compound event.


Classical probability – the use of sample
spaces to determine the numerical
probability that an event will happen.

Equally Likely Events – events that have the
same probability of occurring.

Ex: flipping heads or tails.
Section 4-2
Formula for Classical Probability
The probability of any event E is:
The number of outcomes in E
Total number of outcomes in the sample space
Section 4-2
 Example
5:

A) For a card drawn from an ordinary deck,
find the probability of getting a queen.

B) If a family has three children, find the
probability that all the children are girls
Section 4-2

Example 6: A card is drawn from an ordinary
deck. Find these probabilities:

Of getting a jack

Of getting the 6 of clubs

Of getting a 3 or a diamond

Of getting a 3 or a 6
Section 4-2
 Probability
Rules:

The probability of any event is a number
between (and including) 0 and 1.

If an event cannot occur, then the
probability is 0.

If an event is certain, then the probability is
1.

The sum of the probabilities of all the
outcomes in the sample space is 1.
Section 4-2

Complement of an event – the set of the
outcomes in a sample space that are not
included in the outcomes of the event.


The complement of E is denoted :
E
Example 7: Find the complement of each
event:

Rolling a die and getting a 4.

Selecting a month and getting a month that begins
with J.

Selecting a day of the week and getting a
weekday.
Section 4-2

Empirical probability – probability that relies on
actual experience to determine the likelihood of
outcomes.

also known as experimental probability
Example 8:
In a sample of 50 people, 21 had type O blood, 22
had type A blood, 5 had type B blood, and 2 had
type AB blood.
Set up a frequency distribution and find the following
probabilities:

A person has type O blood

A person has type A or B blood

A person does not have type AB blood
Section 4-2
 Subjective
Probability – a probability
value based on an educated guess or
estimate, employing opinions and inexact
information.
 Ex:
A doctor might say that there is a 30%
chance that a patient will need surgery.
Homework:
 Pg
186: 13, 15, 17 - 21