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Master Probability with Tree Diagrams and Tables

Math 30-2: Master Advanced Algebra & Problem Solving

Rational Expressions

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Partial Fraction Decomposition

Partial fraction decomposition

Solving rational equations

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions 

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Applications of rational equations

Simplifying complex fractions

Polynomial Functions

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Polynomial long division

Polynomial synthetic division 

What is a polynomial function?

Polynomial functions

Recognizing a Polynomial Function

Remainder theorem

Finding the Remainder Using Synthetic Division and the Remainder Theorem

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials 

Imaginary zeros of polynomials

Solving polynomial inequalities

Fundamental theorem of algebra

Exponential Functions

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule (a^x / a^y) = a^(x-y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule (a^x)^y = a^(x * y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Exponents: Negative exponents

Exponents: Zero exponent: a^0 = 1

Exponents: Zero exponent: a^0 = 1

Exponents: Rational exponents

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Solving exponential equations using exponent rules

Logarithmic Functions

Solving logarithmic equations

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Graphing logarithmic functions

Finding a logarithmic function given its graph

Applications of Exponential and Logarithmic Functions

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Data Collection

Influencing factors in data collection

Data collection

Introduction to probability

Permutations and Combinations

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Permutation vs. Combination

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Introduction to probability 

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability with permutations and combinations

Probability involving permutations and combinations

Probability with Venn diagrams

Scatter Plots and Best Fit Line

Bivariate, scatter plots and correlation 

Regression analysis

Equation of the best fit line

Reciprocal Functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Math 30-2 (Alberta)

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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-ca-math-30-2.png

Intro

Ex. 1:

Ex. 2:

Ex. 3:

- Hi, welcome to this question right here. So what happened is, I actually did the answer already. But let's just go through the question and see what happens. Right? 
So Ken over here flips a coin. And we know that there's only head and tail on the coin. Right? So basically what happened is at the very beginning you had to get a head or you had to get a tail. Okay? Then you can go to a bag the contents. Find different marbles, each with different colors. And we&apos;ve got the green, the blue, red, orange and the yellow. Okay? So what happened is after you do this, you flip the head. There's a possibly that you can get a green, blue, red, orange or yellow. Right? Same thing with the tail. Okay? 
Once you flipped the tail. You might get a green, blue, red, orange or the yellow. Right? So the total sample space you're going to have for this question is just going to be these guys over here. Total of 10. Okay? We&apos;ve got a head and green, head and blue, head and red, head and orange, head and yellow. And of course got a tail and a green, tail/blue, tail/red, tail/orange and tail and yellow. Okay? So this is the tree diagram for this sample space. Okay? 
Thanks for watching.

Tables and tree diagrams are useful tools to calculate probabilities. With them, you can list all the possible outcomes of an event (<a href='[[glossary.html|{"keyword":"Sample Space"}]]'>sample space</a>) in a clear and easy to understand way. Therefore, we can determine the probabilities of events effectively.

Using tables and tree diagrams for probability