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.

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