Probability

Learning Topics: 

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

This page lists the Learning Objectives for all 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.