VCE Maths Methods Units 1-4: Probability

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Become a master in probability in your Maths Methods exam!

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What Will I Learn?

- Understand the basics of probability and be able to draw a sample space
- Draw tree diagrams
- Draw Karnaugh maps
- Use the addition law of probability
- Distinguish between mutually exclusive events and independent events
- Calculate conditional probabilities
- Count using the addition and multiplication principles
- Count using permutations (nPr)
- Count using combinations (nCr)
- Discrete random variables: Draw a probability distribution table; calculate probabilities; calculate the mean/expected value, median, mode, variance and standard deviation (including linear transformations on the mean and variance)
- Binomial distribution: Calculate probabilities; calculate the mean/expected value, variance and standard deviation
- Continuous random variables: Draw the graph of a probability density function (pdf); acknowledge that the area beneath a pdf is 1; calculate probabilities, calculate the mean/expected value, median, mode, variance and standard deviation
- Normal distribution: Calculate probabilities (including by symmetry of the normal distribution graph without the aid of a calculator); appreciate the standard normal distribution; calculate using the inverse normal distribution
- Statistical inference: Distinguish between population and sample size/proportion; describe the distribution of p̂ and calculate probabilities associated with it; write confidence intervals
- MOREOVER, students at a unit 3/4 level will also learn how to approach worded problems comprised of multiple parts, and learn how to use a graphics calculator in relation to probability calculations.

Requirements

- For students wanting to cover the unit 1/2 content of this course, there are no course requirements, although a basic understanding of probability would be useful.
- For students wanting to cover the unit 3/4 content of this course, they need to have a sound understanding of the unit 1/2 content of probability (with an exception for ‘permutations’ as it is not part of the unit 3/4 course).
- Moreover, unit 3/4 students need to be able to sketch the graphs of basic functions (including hybrid functions), and evaluate definite integrals. This is necessary for the lectures under the topic ‘continuous random variables’.
- A graphics calculator is generally required for the unit 3/4 content.

Description

After going through this course, you will be able to understand how probability works at an Australian VCE Maths Methods Units 1-4 level, and apply such knowledge on exam questions. Each lecture includes many clearly annotated diagrams to make mathematical concepts easier to understand, and will be followed by a quiz to test your understanding.

The lectures are designed to cater for both unit 1/2 students and unit 3/4 students, with the unit 1/2 and unit 3/4 content indicated at the beginning of each ‘section’ of this course. Unit 1/2 students only need to watch the unit 1/2 content of each lecture, although you may go on to watch the unit 3/4 content if you want to get a head start. Unit 3/4 students may find the unit 1/2 content a good revision for them.

You are encouraged to go through the lectures in order since the content from the earlier lectures is often required in the later lectures.

Who is the target audience?

- This course mainly caters for students doing the Australian VCE subject, Mathematical Methods unit 1/2 and 3/4.
- However, students from other countries or Australian states at a level equivalent to year 11 and 12 in Australia may also find this course useful.
- This course will clearly outline the content from unit 1/2 and unit 3/4, although sometimes there is a slight overlap between the two. For unit 1/2 students, you can also watch the unit 3/4 content to get a head start for the future; while for unit 3/4 students, you can also watch the unit 1/2 content if you need some revision on the previously learnt material.

Compare to Other Probability Courses

Curriculum For This Course

20 Lectures

03:49:07
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Introduction
1 Lecture
03:08

This lecture provides an introduction to the course.

Preview
03:08

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Unit 1/2 Probability
7 Lectures
01:26:51

This lecture introduces the basics of probability that you would have covered in year 10. You will learn how to write down a sample space, distinguish between mutually exclusive events and independent events, and draw tree diagrams.

If you don’t have a very strong foundation on probability, this lecture will act as a good revision for you. However, unit 3/4 students are also highly encouraged to watch the example involving tree diagrams (from 10:34 minutes onwards) as it acts as a good exam question.

Probability basics (including tree diagrams)

18:01

Probability basics (including tree diagrams)

6 questions

This lecture introduces the addition law of probability, and teaches you how to draw Karnaugh maps. It also covers how Pr(A∩B) = 0 for mutually exclusive events, and how Pr(A∩B) = Pr(A) × Pr(B) for independent events.

Preview
13:14

Karnaugh maps (including the addition law of probability)

4 questions

This lecture introduces the concept of conditional probability, and teaches you how to apply the concept on theory-based (formula-based) questions and worded problems.

Preview
11:43

Conditional probability

3 questions

This lecture introduces the addition and multiplication principles to calculate the number of ways a task can be performed (e.g. creating a three-digit number from the digits 1, 2, 3, 4, 5 and 6), which can be subsequently used to calculate probabilities. Moreover, factorials are introduced at the end of this lecture, which is necessary for the next two lectures.

Introduction to counting problems

12:23

Introduction to counting problems

7 questions

This lecture teaches you how to count using **permutations** (nPr), which enables you to calculate the number of ways ‘r’ objects can be selected from ‘n’ objects where order is important. Moreover, it will include calculation of probabilities involving permutations.

Counting using permutations

12:49

Counting using permutations

5 questions

This lecture teaches you how to count using **combinations** (nCr), which enables you to calculate the number of ways ‘r’ objects can be selected from ‘n’ objects where order is NOT important. *Part one* of this lecture will introduce the basics of combinations, and teach you how to calculate combinations (e.g. 10C4).

Counting using combinations (part one)

08:43

This lecture teaches you how to count using **combinations** (nCr), which enables you to calculate the number of ways ‘r’ objects can be selected from ‘n’ objects where order is NOT important. *Part two* of this lecture will focus on worded problems involving combinations, including the calculation of probabilities.

Counting using combinations (part two)

09:58

Counting using combinations

5 questions

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Unit 3/4 Probability
10 Lectures
02:01:03

Content:

- Introduction: Discrete random variables vs. continuous random variables

- Discrete probability distribution tables

- Calculating probabilities

Discrete random variables (part one)

10:42

Content:

- Calculating the mean (expected value), median and mode

- Calculating the variance (and standard deviation)

Note: This lecture also goes through the *linear transformations* of the expected value and the variance.

Discrete random variables (part two)

12:45

This video goes through a worded problem on discrete random variables. Highly recommended as a **practice exam question**!

Discrete random variables (worded problem)

10:29

Discrete random variables

8 questions

Content:

- Conditions for a variable to be binomially distributed

- Calculating probabilities

- Calculating the mean and standard deviation

Binomial distribution

16:09

This video goes through a few slightly more complicated examples relating to the binomial distribution, which are the type of questions you would expect to find in the exam. Highly recommended as **practice exam questions**!

Binomial distribution (more complicated examples)

07:10

Binomial distribution

7 questions

Content:

- Features of a probability density function

- Calculating probabilities

- Calculating the mean (expected value), median and mode

- Calculating the variance (and standard deviation)

Continuous random variables

16:19

This video goes through a worded problem on continuous random variables (probability density functions). Highly recommended as a **practice exam question**!

Continuous random variables (worded problem)

12:23

Continuous random variables

6 questions

Content:

- Properties of the normal distribution

- Calculating probabilities

- Standard normal distribution

Normal distribution (part one)

10:21

Content: Part two

- Calculating probabilities *using symmetry of the normal distribution graph*

- Inverse normal distribution (includes finding the mean or standard deviation)

Normal distribution (part two)

11:53

This video goes through a worded problem on the normal distribution. Highly recommended as a **practice exam question**!

Normal distribution (worded problem)

12:52

Normal distribution

8 questions

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Unit 3/4 Statistical Inference
2 Lectures
18:05

Content:

- Introduction to population proportion and size vs. sample proportion and size (part one)

- The distribution of p̂, including the calculation of probabilities associated with it (part one)

- Confidence intervals (part two)

Statistical inference (part one)

11:25

Content:

- Introduction to population proportion and size vs. sample proportion and size (part one)

- The distribution of p̂, including the calculation of probabilities associated with it (part one)

- Confidence intervals (part two)

Statistical inference (part two)

06:40

Statistical inference

4 questions