This page lists the Learning Objectives for the lessons in Unit 6 of 14.
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 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 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 each of five 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 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 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 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 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.
- Compute conditional probabilities to solve problems.
Practice Exercises
The student will be able to:
- Determine which formulas and procedures are needed to complete each practice exercise for this unit.
- 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:
- 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.
- Compare solutions to those completed.
- 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.
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