Objective 1: I Can Identify the Sample Space of a Probability Experiment

Statistics3.1: 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

Read Example 1, pg 132.

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 ______.

Read Example 2, pg 133

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?