About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Accessibility

Master Probability of Independent Events: Key Concepts & Tips

CC.HSS.CP.A.2

Probability of independent events

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

auto-gen

CC.HSS.CP.A.3

Conditional probability

CC.HSS.CP.A.5

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

CC.HSS.CP.B.7

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

CC.HSS.CP.B.9

Permutations

Combinations

Probability involving permutations and combinations

CC.HSS.IC.A.1

Sampling methods

Sampling Methods

CC.HSS.IC.A.2

Sampling distributions

Understanding Proportions and Sample Size

Rare event rule

The Rare Event Rule for the Central Limit Theorem

CC.HSS.IC.B.3

Census and bias

Census and Bias

Classifying Bias

CC.HSS.IC.B.4

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

CC.HSS.IC.B.5

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Analysis of variance (ANOVA)

CC.HSS.IC.B.6

Influencing factors in data collection

CC.HSS.ID.A.1

Frequency distribution and histograms

Equation of the best fit line

The determinant of a 2 x 2 matrix

CC.HSS.ID.A.2

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Application of Means

Range and outliers

Range and Outlier Word Problems

Outlier Word Problems

Range Word Problems

Find the Range

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

CC.HSS.ID.A.3

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Shapes of distributions

CC.HSS.ID.A.4

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

CC.HSS.ID.B.5

Reading and drawing Venn diagrams

Probability with Venn diagrams

CC.HSS.ID.B.6

Reading and drawing line graphs

Reading Line Graphs

Bivariate, scatter plots and correlation

CC.HSS.MD.A.1

Probability distribution - histogram, mean, variance & standard deviation

CC.HSS.MD.A.2

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

CC.HSS.MD.A.3

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

CC.HSS.MD.B.7

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Parent Assignments

Challenge Zone

Foundation Review

Statistics and Probability

math

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.

Spinner and marble bag: multiplying independent probabilities

Finding probability of not landing on section 3 and not getting black marble

Finding probability of landing on 1 or 4 and drawing red or blue

Spinner and white marble independent probability calculation

Finding probability of flipping heads and spinning yellow

Finding probability of not getting tail, three, or blue

Finding P(tail, six, and red) using the multiplication rule

Finding P(tail, 2, not blue) using the multiplication rule

Finding probability of NOT getting head, five, or green

Experimental probability of getting a doll from a toy vending machine

Finding the theoretical probability of picking the doll

Comparing experimental and theoretical probability and improving accuracy

Calculating probability of getting the same toy twice in a row

Independent vs dependent events in probability

Addition and multiplication rules for combining probabilities

Theoretical vs experimental probability with coins and dice

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: Mastering Key Concepts

What You'll Learn

Identify independent events where outcomes do not affect each other

Calculate probabilities by multiplying independent event probabilities

Distinguish between independent and dependent events in probability scenarios

Apply the multiplication rule to find combined probabilities of multiple events

What You'll Practice

Finding probabilities using spinners, dice, and coins together

Calculating probabilities of multiple independent events in sequence

Determining whether to multiply or add probabilities based on event types

Solving real-world probability problems with vending machines and games

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

16 Video lessons

Learning resources

Skills

Independent Events

Probability

Multiplication Rule

Sample Space

Tree Diagrams

Compound Events