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Master Probability of Independent Events: Key Concepts & Tips

Grade 12 Math: Master Advanced Concepts & Skills

Role of statistical thinking in research and scientific method

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Determining probabilities using tree diagrams and tables

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Common graphical representations of variation

Frequency tables and dot plots

Analyze the Frequency Table

Frequency distribution and histograms

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Bivariate, scatter plots and correlation

Reading and drawing Venn diagrams

Stem and leaf plots

The Leaf and Stem of Numbers

Recognizing the Leaf and Stem of Numbers

Recognizing The Leaf And Stem of Numbers Leaf

Recognizing The Leaf And Stem of Numbers Stem

Reading Stem and Leaf Plots — Median

Reading Stem and Leaf Plots — Range

stem and leaf plots Range

Reading Stem and Leaf Plots

Reading Stem and Leaf Plots — Mean

Reading Stem and Leaf Plots — Mode

Frequency polygons

Shapes of distributions

Use of summary statistics to describe variation

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Probability distribution - histogram, mean, variance & standard deviation

Association between two variables

Regression analysis

Equation of the best fit line

Probability models for variation

Probability of independent events

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

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

Sampling distributions

Understanding Proportions and Sample Size

Central limit theorem

Central Limit Theorem

Applying the Central Limit Theorem

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Bayes' rule

Bayes" Rule

Bayes rule

Bayes" rule

Bayes' Rule

Poisson distribution

Poisson Distribution

Geometric distribution

Negative binomial distribution

Negative Binomial Distribution

Determining the Negative Binomial Distribution

Determining the Cumulative Negative Binomial Distribution

Hypergeometric distribution

Determining the Cumulative Hypergeometric Distribution

Hypergeometric Distribution

Probability with Venn diagrams

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

Intuition and appreciation of inferential concepts

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Rare event rule

The Rare Event Rule for the Central Limit Theorem

Chi-Squared confidence intervals

Chi-Squared Confidence Intervals

Confidence intervals to estimate population mean

Student's t-distribution

Student"s t-distribution

Determining a Confidence Interval for a Population Mean using t-distributions

Communication of statistical findings

Null hypothesis and alternative hypothesis

Proving claims

Confidence levels, significance levels and critical values

Test statistics

Traditional hypothesis testing

Traditional Mean Hypothesis Testing

P-value hypothesis testing

Proportion Hypothesis Testing

Chi-Squared hypothesis testing

Variance Hypothesis Testing

Chi-Squared Hypothesis Testing

Mean hypothesis testing with t-distribution

Hypothesis Testing Mean Claims without Knowing <katex> \sigma </katex>

Analysis of variance (ANOVA)

Chi-square goodness of fit test

Type 1 and type 2 errors

Type 1 and Type 2 Errors

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Statistics 12

math

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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