9. Sequences, Induction, and Probability

Compute Theoretical Probability

Probability

Calculating the Probability of Simple Events

If you toss a fair coin six times, what is the probability of getting all heads?

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood for three consecutive years?

In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.

In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.

Use the Addition Rule to calculate the probability of disjoint event A or B

Math Probability lectures - Problem solving

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

Calculate probabilities by using the complement and addition rule

Find the probability of a compound event by creating a tree diagram

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a picture card.

In Exercises 39–44, you are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.

Theoretical Probability, Permutations and Combinations

Calculating Probability - " And " statements, Dependent

Find the probability of a compound event by creating an organized list

Probability Tree Diagram

In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a queen.

Compare theoretical and empirical results

In Exercises 21–22, a fair coin is tossed two times in succession. The sample space of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting two heads.

In Exercises 17–20, you are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card.

A die is rolled. Find the probability of getting a number less than 3 or greater than 4.

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood two years in a row?

In Exercises 45-46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 6.<img class="fr-dib" src="https://lightcat-files.s3.amazonaws.com/problem_images/8c6fb26ba45b4ef0-1678243915984.jpg" style="width: 300px;">

In Exercises 11–16, a die is rolled. Find the probability of getting a 4.

Determine the probability of an event and its complement

Solve word problems using the addition rule

Find the probability of a compound event by creating a table

Basic Conditional Probability Example

The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of no flooding for four consecutive years?

In Exercises 49–52, a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.

Probability Problem Involving ' At Least ' and ' Complements '

Calculating Probability - "At Least One" statements

You are dealt one card from a 52-card deck. Find the probability of getting an ace or a king.

A die is rolled. Find the probability of getting a number less than 5.

What is the probability of a family having five boys born in a row? (Assume the probability of a male birth is 1/2.)

Introduction to Random Variables

Finding the Probability of Winning the Texas Lottery

Calculate different probabilities by working backward

Learn the toughest concepts covered in Algebra with step-by-step video tutorials and practice problems by world-class tutors

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1. Fundamental Concepts of Algebra

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Find the Common Difference for an Arithmetic Sequence

Write Terms of an Arithmetic Sequence

Use the Formula for the General Term of an Arithmetic Sequence

Use the Formula for the Sum of the First n Terms of an Arithmetic Sequence

Arithmetic Sequences

Compute Empirical Probability

Find the Probability that an Event will Not Occur

Find the Probability of One Event or a Second Event Occurring

Find the Probability of One Event and a Second Event Occurring

Evaluate a Binomial Coefficient

Expand a Binomial Raised to a Power

The Binomial Theorem

Use the Fundamental Counting Principle

Distinguish Between Permutation and Combination Problems

Use the Permutations Formula

Counting Principles, Permutations, and Combinations

Find Particular Terms of a Sequence from the General Term

Use Recursion Formulas

Use Factorial Notation

Use Summation Notation

Sequences and Summation Notation

Understand the Principle of Mathematical Induction

Prove Statements Using Mathematical Induction

Mathematical Induction

Find the Common Ratio of a Geometric Sequence

Write Terms of a Geometric Sequence

Use the Formula for the General Term of a Geometric Sequence

Use the Formula for the Sum of the First n Terms of a Geometric Sequence

Find the Value of an Annuity

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Geometric Sequences and Series

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