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Master Probability of Independent Events: Key Concepts & Tips

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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Intro

Ex. 1:

Ex. 2:

Ex. 3:

- Hi and welcome to this question right here. So this is a very fun exercise, okay? So you got a spinner divided into the four equal parts and you're going to spin it. And each section is labeled one, two, three and four. You got another marble drawn from the bag over here that has five different marbles, color of the green, the red, the blue, the black, and the white. So your task is to figure the probability that you want to land on section two and getting a green marble, okay? If you're trying to figure out the probability of the two events, that's one event right here. That's a second event. So you're doing something twice. So all you got to do is just multiply the probability together, okay? 
So let's take a look at how to get a section two right here. Well the spinner right here it's divided into four equal parts, right? So what happened is you want to get a two. There's only one of them, right? That's one of the four possibilities to get a two right there. It's actually the same possibility for all the numbers, actually. Now you're going to multiply, okay? Because, again, remember this. This is two different events. They are called independent because what that means is the outcome from the first event does not affect the second event, okay? So basically, me drawing the green from here is not affected by the spinning right here. It doesn't affect me at all, okay? So when you have two different independent events you're going to multiply them together. Multiply the probabilities together. The second one right here wants you to get the green marble. Well how many greens do you have? You got one. So that's the one that you're looking for. How many possibilities do you have in this bag? 
You have five marbles, right? 
So that's your total sample base. You put it right at the bottom, okay? 
At the very end, guess what happened? 
Multiply. One times one gives you just one and divided by the four times five gives you 20. So the chance for you to spin the two and then grab a green from the bag without looking at it is just 1 of the 20 of the chance. Not a good odd but still better than 649. Thanks for watching.

Probability is everywhere in our daily life. Do you know your chances of winning a specific prize in a spinning wheel prize draw? How about the odd to get the same prize two times in a row? By applying the concept of probability of independent events, we can easily answer these questions.

Probability of independent events 

Probability of independent events (advanced)

Probability of independent and combined events

Probability of Independent Events Examples