Probability

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.

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