Statistics
3.1: Basic Concepts of Probability and Counting
Objective 1: I can identify the sample space of a probability experiment.
A probability experiment is
An outcome is
The sample space of a probability experiment is
An event is
A simple event is
In this chapter you will learn how to calculate the probability or ____________________ of an event.
Events are often represented by _____________ letters, such as ____, ____, or ____. An event that
consists of a single outcome is called a ___________ event. The event “tossing heads and rolling a 3” is
a simple event because it can be represented as ________. However, the event “tossing a heads and
rolling an even number” is not a simple event, as it can be represented by
___________________________.
TIY 2: You ask for a student’s age at his or her last birthday. Decide whether each event is simple or
not.
1. Event C: The student’s age is between 18 and 23, inclusive.
2. Event D: The student’s age is 20.
Objective 2: I can use the fundamental counting principle to find the number of ways an event
can occur.
In some cases, an event can occur in so many different ways that it is not practical to write out all of the
outcomes. When this occurs we use the Fundamental Counting Principle to find the
_________________________________________________________________________.
If one event can occur in ____ ways and a second event can occur in ____ ways, then the number of
ways the two events can occur in sequence is _________. This rule can be extended for any number of
events, not just two, that occur in sequence.
Read Example 3, pg 134.
TIY 3: You go to Applebee’s and get a combo—an appetizer, an entrée, and a dessert. If there are 6
choices for an appetizer, 11 choices for an entrée, and 4 choices for dessert, how many different meals
can be created?
Read Example 4, pg 135
TIY 4: How many license plates can you make if a license plate consists of
1. six alphabet letters each of which can be repeated?
2. six alphabet letters each of which cannot be repeated?
3. 4 numbers followed by 2 alphabet letters, all of which can be repeated?
Objective 3: I can distinguish between the three types of probability.
How we calculate probability depends on the type of probability. The probability that event E will occur
is written as ________ and read “_______________________________________”. (Read “Study Tip”
on page 136.) There are three types of probability:
i) Classical, or ________________, probability is used when each ___________ in the sample space is
____________________ to occur. The probability of an event, E, is given by
*We use classical probability to determine “what should happen” before an event is performed.
Read Example 5, pg 136
TIY 5: You select a card from a standard deck. (See pg 136) Find the probability of each event.
1. Event D: Selecting a seven of diamonds.
2. Event E: Selecting a diamond.
3. Event F: Selecting a diamond or heart.
ii) Empirical, or ______________ probability, is probability based on _________________ obtained
from a probability experiments. The empirical probability of an event, E, is the
____________________________ of the event and is given by
*We use empirical probability to determine “what did happen” after an event takes place.
Read Example 6, pg 167
TIY 6: An insurance company determines that in every 100 claims, 4 are fraudulent. What is the
probability that the next claim the company receives will be fraudulent?
As you increase the number of times a probability experiment is repeated, the _______________
probability of an event approaches the ___________________ probability of the event. This is known
as the _________________________________. (Read top half of page 138 for further explanation of
this.)
We can also find probability using a frequency distribution.
Read Example 7, pg 138
TIY 7: Find the probability that an employee chosen at random will be between 35 and 64 years old.
iii) _________________ probability comes from _____________________________________.
*We use subjective probability to determine “what I think will happen”.
Read Example 8, pg 139
TIY 8: Based on previous counts, the probability of a salmon successfully passing through a dam on the
Columbia River is 0.85. Which type of probability is this statement describing?
If you look back at the answers to the probabilities that we have found, you may notice that probability
is always ________________. The probability of an event must be _____________, that is
_________________.
Here is a chart that shows the possible range of probabilities and their meanings.
An event that occurs with a probability of ______ or less is typically considered ____________.
Unusual events are highly unlikely to occur.
Objective 4: I can find the probability of complementary events.
The sum of the probabilities of ALL outcomes in a sample space is _____ or ________. An important
result of this fact is that if you know the probability of an event E, you can find the probability of the
________________ of event E.
The _________________ of event E is the set of all outcomes in a sample space that are
___________________________________. The complement of event E is denoted ______ and is read
as ____________.
Quick Example:
1) If you roll a die and the event is “roll an even number” then the complement of the event is:
2) If you draw a card and the event is “draw a clubs”, then the complement if the event is:
Read Example 9, pg 140.
TIY 9: Use the frequency distribution below to find the probability of randomly choosing an employee
who is not between 45 and 54 years old.
Objective 5: I can find probability of events using tree diagrams or the fundamental counting
principle.
Read Example 10 and 11 on page 141.
TIY 10: Find the probability of tossing a tail and spinning a number less than 6.
TIY 11: Your college ID number consists of 8 digits. Each digit can be 0 through 9 and each digit can
be repeated. What is the probability of guessing your ID number when randomly generating eight
digits?