## Learning Topics:

Introduction, certain and impossible events, sample spaces, complement, mutually exclusive events, addition rules, independent and dependent events, conditional probability.

## Learning Objectives for all Probability Lessons in Unit 6.

**Introduction to Probability**

The student will be able to:

- Define experiment, outcome, event, probability and equally likely.
- Restate the formula for finding the probability of an event.
- Determine the outcomes and probabilities for experiments.
- Interact with die rolls and spinners to help predict the outcome of experiments.
- Distinguish between an event and an outcome for an experiment.
- Recognize the difference between outcomes that are equally likely and not equally likely to occur.
- Apply probability concepts to complete five interactive exercises.

**Certain and Impossible Events**

The student will be able to:

- Define certain event, impossible event.
- Describe and list the contents of a standard deck of 52 playing cards.
- Examine the probabilities of experiments with certain outcomes.
- Examine the probabilities of experiments with impossible outcomes
- Evaluate interactive die rolls and spinners in relation to certain and impossible events.
- Explain the difference between certain and impossible events.
- Compute the probability of a certain event.
- Compute the probability of an impossible event.
- Apply concepts to complete five interactive exercises.

**Sample Spaces**

The student will be able to:

- Define sample space.
- Examine the sample space and probabilities for experiments.
- Recognize that the sum of the probabilities of the distinct outcomes within a sample space is one.
- Determine the sample space of an experiment to complete five interactive exercises.

**The Complement of an Event**

The student will be able to:

- Define the complement of an event.
- Identify the complement of an event by examining the sample space for that event.
- Describe the formula for finding the probability of the complement of an event.
- Examine experiments in which the complement of an event is determined and its probability is computed.
- Recognize the relationship between the sample space of an experiment and the complement of an event.
- Compute the probability of the complement of an event.
- Apply the formula for finding the complement of an event to compute probabilities in each of five interactive exercises.

**Mutually Exclusive Events**

The student will be able to:

- Define mutually exclusive events.
- Examine experiments in which the events are mutually exclusive.
- Examine experiments in which the events are not mutually exclusive.
- Distinguish between mutually exclusive events and non-mutually exclusive events.
- Determine whether two events are mutually exclusive or non-mutually exclusive.
- Connect set theory and Venn diagrams with events that are mutually and non-mutually exclusive.
- Identify events as mutually or non-mutually exclusive in each of five exercises.

**Addition Rules for Probability**

The student will be able to:

- Restate Addition Rule 1 for computing the probability of a mutually exclusive event.
- Examine experiments in which Addition Rule 1 is applied to compute probabilities of mutually exclusive events.
- Restate Addition Rule 2 for computing the probability of a non-mutually exclusive event.
- Examine experiments in which Addition Rule 2 is applied to compute probabilities of non-mutually exclusive events.
- Summarize the procedures for applying the addition rules to compute probabilities of events that mutually or non-mutually exclusive.
- Compute probabilities by applying addition rules.
- Apply addition rules to compute probabilities in five interactive exercises.

**Independent Events**

The student will be able to:

- Define independent events, compound events and replacement.
- Give examples of independent events.
- Restate Multiplication Rule 1 for finding the probability of independent events.
- Examine experiments in which the probability of two independent events is computed.
- Examine experiments in which the probability of three independent events is computed.
- Explain the relationship between replacement and independent events.
- Compute the probability of independent events.
- Apply Multiplication Rule 1 to find the probability of independent events in each of five interactive exercises.

**Dependent Events**

The student will be able to:

- Define dependent events and conditional probability.
- Restate the Multiplication Rule 2 for finding the probability of dependent events.
- Examine experiments in which the probability of two dependent events is computed.
- Examine experiments in which the probability of three or four dependent events is computed.
- Examine experiments without replacement.
- Explain the relationship between conditional probability and dependent events.
- Compute the probability of dependent events.
- Apply Multiplication Rule 2 to find the probability of dependent events in each of five interactive exercises.

**Conditional Probability**

The student will be able to:

- Review the definition of conditional probability and Multiplication Rule 2.
- Interpret the derivation of the conditional probability formula from Multiplication Rule 2.
- Examine experiments in which a conditional probability is computed using the formula.
- Connect set theory and Venn diagrams with conditional probability.
- Evaluate five interactive exercises with word problems.
- Analyze each word problem to identify the given information.
- Formulate a strategy for solving each problem.
- Compute conditional probabilities to solve problems.

**Practice Exercises**

The student will be able to:

- Examine ten interactive exercises for all topics in this unit.
- Determine which formulas and procedures are needed to complete each practice exercise.
- Compute answers by applying appropriate formulas and procedures.
- Self-assess knowledge and skills acquired from this unit.

**Challenge Exercises**

The student will be able to:

- Evaluate ten interactive exercises with word problems for all topics in this unit.
- Analyze each word problem to identify the given information.
- Formulate a strategy for solving each problem.
- Apply strategies to solve routine and non-routine problems.
- Synthesize all information presented in this unit.
- Connect probability to the real world.
- Develop problem-solving skills.

**Solutions**

The student will be able to:

- Examine the solution for each exercise presented in this unit.
- Identify which solutions need to be reviewed.
- Compare solutions to completed exercises.
- Identify and evaluate incorrect answers.
- Amend original answers.
- Identify areas of strength and weakness.
- Decide which concepts, formulas and procedures need to be reviewed from this unit.