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Introduction

Welcome to Explorer Math Grade 12 Statistic & Data Management (MDM4U) Level 7C

Introduction to Probability

Lesson 1: How probabilities are used to represent the likelihood of a result of an experiment or a real-world event

Lesson 1 Power Math

(GRADED) Lesson 1 Quiz

Lesson 2: Sample space as a set that contains all possible outcomes of an experiment

Lesson 2 Power Math

(GRADED) Lesson 2 Quiz

Lesson 3: Distinguish between a discrete sample space and a continuous sample space

Lesson 3 Power Math

(GRADED) Lesson 3 Quiz

Lesson 4: Using appropriate notation and terminology pertaining to sets of data and set theory

Lesson 4 Power Math

(GRADED) Lesson 4 Quiz

Lesson 5A: Using probability formulas to complement visual problem-solving methods

Lesson 5A Power Math

(GRADED) Lesson 5A Quiz

Lesson 5B: Using probability formulas to complement visual problem-solving methods

Lesson 5B Power Math

(GRADED) Lesson 5B Quiz

Lesson 6: Determining the theoretical probability, P (i.e., a value from 0 to 1), of each outcome of a discrete sample space

Lesson 6 Power Math

(GRADED) Lesson 6 Quiz

Lesson 7: Determining the complement of an event

Lesson 7 Power Math

(GRADED) Lesson 7 Quiz

Lesson 8: Recognizing that the probabilities P form the probability distribution associated with the sample space

Lesson 8 Power Math

(GRADED) Lesson 8 Quiz

Lesson 9: Recognizing and describing an event as a set of outcomes and as a subset of a sample space

Lesson 9 Power Math

(GRADED) Lesson 9 Quiz

Lesson 10: Solve theoretical probability problems

Lesson 10 Power Math

(GRADED) Lesson 10 Quiz

Lesson 11: The difference (and connection) between experimental and theoretical probability

Lesson 11 Power Math

(GRADED) Lesson 11 Quiz

Lesson 12: Determining the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases

Lesson 12 Power Math

(GRADED) Lesson 12 Quiz

Lesson 13: Reflecting on the role of probability in predictions and decision making

Lesson 13 Power Math

(GRADED) Lesson 13 Quiz

Lesson 14: When and how to use Venn diagrams as an aid to problem solving

Lesson 14 Power Math

(GRADED) Lesson 14 Quiz

Lesson 16: Constructing tree diagrams as a aid to problem solving

Lesson 16 Power Math

(GRADED) Lesson 16 Quiz

Lesson 17: Investigating connections between various ways of approaching problems (diagrams, formulas) and judging which is best

Lesson 17 Power Math

(GRADED) Lesson 17 Quiz

Lesson 18: Distinguishing between mutual exclusive and independence

Lesson 18 Power Math

(GRADED) Lesson 18 Quiz

Lesson 19: Determining whether two or more events are mutually exclusive or non-mutually exclusive

Lesson 19 Power Math

(GRADED) Lesson 19 Quiz

Lesson 20: Solving Probability Problems for P(A′), P(A and B), and P(A or B) Using Venn Diagrams, Lists & Formulas

Lesson 20 Power Math

(GRADED) Lesson 20 Quiz

Lesson 21: Understanding and applying the symbols and criteria for independent and dependent events

Lesson 21 Power Math

(GRADED) Lesson 21 Quiz

Lesson 26: Calculating and using conditional probabilities in simple cases

Lesson 26 Power Math

(GRADED) Lesson 26 Quiz

Lesson 27: Probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate)

Lesson 27 Power Math

(GRADED) Lesson 27 Quiz

Lesson 29: Understanding the terms permutation and combination

Lesson 29 Power Math

(GRADED) Lesson 29 Quiz

Lesson 30A: Recognizing the use of permutations and combinations in counting (Part 1)

Lesson 30A Power Math

(GRADED) Lesson 30A Quiz

Lesson 30B: Recognizing the use of permutations and combinations in counting (Part 2)

Lesson 30B Power Math

(GRADED) Lesson 30B Quiz

Lesson 37: Solving problems about arrangements of objects in a line, including those involving repetition and restriction

(GRADED) Lesson 37 Quiz

Lesson 38: Solving introductory counting problems involving the additive counting principle

(GRADED) Lesson 38 Quiz

Lesson 39: Solving introductory counting problems involving the multiplicative counting principle

(GRADED) Lesson 39 Quiz

Lesson 40: Addition and multiplication of the probabilities of mutually exclusive events and independent events

(GRADED) Lesson 40 Quiz

Lesson 41: Using addition and multiplication of probabilities in simple cases

(GRADED) Lesson 41 Quiz

Lesson 43: Connecting Combinations (n Choose r) and Pascal’s Triangle Through Investigation, Addition & Multiplication of Probabilities

(GRADED) Lesson 43 Quiz

Math Check-In

Chapter 1: Probability

Lesson 1: Calculating and interpreting z-scores-2

Lesson 1 Power Math-5

Lesson 2: Understanding z-Scores as Standard Deviations from the Mean & Solving Probability Problems with Normal Distributions

Lesson 2 Power Math-3

Lesson 3: Understanding the concept of a continuous random variable versus discrete random variable-2

Lesson 3 Power Math-4

Lesson 4: Identifying a discrete random variable X

Lesson 4 Power Math-4

Lesson 5: Generating Probability Distributions by Calculating Probabilities for All Values of a Random Variable, With or Without Technology

Lesson 5 Power Math-3

(GRADED) Lesson 5 Quiz

Lesson 6: Creating a probability distribution table and probability distribution histogram

Lesson 7: Calculating weighted average

Lesson 7 Power Math-2

Lesson 8: Calculating the expected value for a given probability distribution and interpret the expected value in applications,

Lesson 8 Power Math-2

Lesson 11: Making connections between the frequency histogram and the probability histogram (e.g., by comparing their shapes)

Lesson 11 Power Math-2

Lesson 12: Identifying Binomial Probability Conditions & Calculating Probabilities for Each Value of the Random Variable

Lesson 12 Power Math-2

Lesson 13: Representing Binomial Distributions with Tables, Probability Histograms & Algebraic Expressions

Lesson 13 Power Math-2

Lesson 14: Identifying Hypergeometric Distribution Conditions & Calculating Probabilities for Each Value of the Random Variable

Lesson 15: Representing the hypergeometric distribution numerically using a table and graphically using a probability histogram

Lesson 15 Power Math-2

Lesson 16: Comparing with technology and using numeric and graphical representations, the probability distributions of discrete random variables

Lesson 17: Solving problems involving probability distributions (e.g., uniform, binomial, hypergeometric) (In the lesson use real-world applications)

Lesson 17 Power Math-2

Lesson 18: Creating Probability Distribution Tables for Discrete Random Variables & Calculating E(X) and Var(X)

Lesson 18 Power Math-2

Lesson 20: Binomial distribution

Lesson 20 Power Math-2

Lesson 21: Making connections between patterns in Pascal’s triangle and coefficients in binomial expansions

Lesson 21 Power Math-2

Lesson 23: Using the binomial theorem to solve problems involving binomial expansions

Lesson 23 Power Math

(GRADED) Lesson 23 Quiz

Lesson 24: Using the GDC to calculate probability, expected value, standard deviation in binomial experiments

Lesson 25: Normal (Gaussian) distribution (In the lesson look at: when it is useful, roles of the mean and standard deviation, 68-95-99.7 rule)

Lesson 25 Power Math

(GRADED) Lesson 25 Quiz

Lesson 26: The Poisson Distribution

Lesson 26 Power Math-2

Lesson 27: Use formulae to calculate probabilities for the distribution Po (ƛ)

Lesson 27 Power Math-2

Lesson 29: Understanding the relevance of the Poisson distribution to the distribution of random events, and use the Poisson distribution as a model

Lesson 29 Power Math-2

Lesson 30: Using the Poisson Distribution to Approximate the Binomial Distribution When Appropriate

Lesson 30 Power Math

(GRADED) Lesson 30 Quiz

Lesson 31: Using the Normal Distribution with Continuity Correction to Approximate Poisson Distribution (λ > 15)

Lesson 31 Power Math

(GRADED) Lesson 31 Quiz

Lesson 32: Central Limit Theorem: Understanding Sample Mean Variation & Applying the CLT Informally Where Appropriate

Lesson 32 Power Math

(GRADED) Lesson 32 Quiz

Lesson 33: Using simulation software to explore sampling distributions

Lesson 35: Calculating unbiased estimates of the population mean and variance from a sample, using either raw or summarised data

(GRADED) Lesson 35 Quiz

Lesson 36: Understanding Continuous Random Variables & Using Probability Density Functions Over a Single Interval, Including Infinite Domains

Lesson 36 Power Math

(GRADED) Lesson 36 Quiz

Lesson 37: Mean, median, variance of continuous random variables and how to find percentiles

Lesson 37 Power Math

Lesson 42A: Calculating Mean & Standard Deviation from Raw/Grouped Data, Given Totals, and Coded Totals (Part 1)

(GRADED) Lesson 42A Quiz

Lesson 42B: Calculating Mean & Standard Deviation from Raw/Grouped Data, Given Totals, and Coded Totals (Part 2)

(GRADED) Lesson 42B Quiz

Lesson 42C: Calculating Mean & Standard Deviation from Raw/Grouped Data, Given Totals, and Coded Totals (Part 3)

Lesson 42 Power Math

(GRADED) Lesson 42C Quiz

Lesson 43: Challenges of Continuous Frequency Distributions & the Need for Mathematical Models

Lesson 44: Representing, using intervals, a sample of values of a continuous random variable numerically using a frequency table

Lesson 44 Power Math

(GRADED) Lesson 44 Quiz

Lesson 45: Interpretation of data as a boxplot

(GRADED) Lesson 45 Quiz

Lesson 46: Recognizing that theoretical probability for a continuous random variable is determined over a range of values

Lesson 46 Power Math

(GRADED) Lesson 46 Quiz

Chapter 2: Probability Distribution

Lesson 1: Reviewing Terminology (e.g., statistics, parameters, population, sample, census, survey, modal class)

Lesson 2: Understanding the difference between types of bias: sampling and statistical

Lesson 3: Explaining Why Sampling Methods May Be Unsatisfactory & Using Random Numbers to Produce Random Samples

Lesson 4: Distinguishing Population and Sample, Characteristics of a Good Sample & Why Sampling Is Necessary

Lesson 5: Comparing sampling techniques (e.g., simple random, systematic, stratified, convenience, voluntary)

Lesson 6: How Random Sample Biases and Non-Random Samples Affect Study Results (Response, Measurement, Non-Response & Sampling Bias)

Lesson 7: Characteristics of an effective survey and design questionnaires or experiments for gathering data

Lesson 8: Collecting data from primary sources, through experimentation, or from secondary sources

Lesson 9: Organizing data with one or more attributes to answer a question or solve a problem

Lesson 10: Reasons why variability is inherent in data

Lesson 11: Distinguishing between situations that involve one variable and situations that involve more than one variable

Chapter 3: Study Design

Course Code: MDM4UCourse Type: University PreparationFormat: Online School CoursePrerequisite: MCR3U - recommended to better understand the contentCourse Format: Online, Learn at your own pace, built-in supports and prompts, Gamified Learning with Pop Quizzes, Online Exams, Auto-grading, Current Grade Displayed In this course, you will thoroughly explore probabilities and how to analyze, understand, interpret, and apply data. You will be learning how to apply concepts such as proportions and distributions to analyze data and more!This course explores the usage of probabilities in various contexts, alongside exploring the technical side of various ways to actually calculate probabilities. It also equips you with the skills required to set up accurate tests relating to real-life scenarios that will provide useful results. This will allow you to develop an essential skillset of mathematical skills that are highly applicable in real life and in many careers.

MDM4U Statistics & Data Management: University-preparation Ontario course covering probability, distributions, proportions, and statistical testing, with real-world applications, online self-paced learning, supports, quizzes, exams, auto-grading, and grad

MDM4U - Math Grade 12-7C Ontario

MDM4U - Math Grade 12-7C Ontario

Hasina Lookman

Course Details

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Includes