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Master Probability: From Basics to Advanced Concepts

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

- Hi, welcome to this question right here. So, we've got a little survey problem right here, okay? So, 600 people were randomly selected in downtown. So, they were asked if they choose their clothing based on the comfort or the style, okay? 
So, here are your results. We get the male, female, the total from the both. And there's a Style and there's a Total here, and as you can see there's the data, right? 
So, what is the probability that the person in the survey is a female? What that means is you're trying to figure out the probability of a female from this whole population right here, okay? 
Be careful right here. If you read across, these are the males that have chosen the comfort, these are the males that have chosen the style. And this is the total number of the males. And of course, this would be the females right over here which is the total. And this is the total population. So, when you're looking for the probability, there's something that you have to know, the probability is just something that you're interested, on the top, divided by the total population at the bottom, okay? 
Let's start with the total population on the bottom which is 600 people, that have taken the survey, right? It says right it right above, 600 people in total. You're looking for the probability of a female. So, how many females do you have? Right there, 295. Two hundred twenty-five people that have taken the survey, that are females. So, there's your 295 right here, okay? And of course, because you're dealing with probability, usually at the end we would like to refer it as a percentage, okay? 
So, 295 divided by 600 and if you times it by 100 again, to get the percent, we've got 49.17%. And that is the probability of that a person in the survey is a female, okay? Let's check out the next part of the question.

This lesson answers the question:  What are the differences between mean, median and mode in statistics? Also, we will learn how to calculate the probabilities out of a two-way frequency table, and figure out the trends.