# VCE Mathematical Methods Units 1 and 2 – Probability and Statistics

4.1 Probability

4.2 Counting Techniques

## Unit 1

In this area of study, students cover the concepts of event, frequency, probability and representation of finite sample spaces and events using various forms such as lists, grids, Venn diagrams, Karnaugh maps, tables and tree diagrams. This includes consideration of impossible, certain, complementary, mutually exclusive, conditional and independent events involving one, two or three events (as applicable), including rules for computation of probabilities for compound events.

This area of study includes:

- random experiments, sample spaces, outcomes, elementary and compound events
- simulation using simple random generators such as coins, dice, spinners and pseudo-random generators using technology, and the display and interpretation of results, including informal consideration of proportions in samples
- probability of elementary and compound events and their representation as lists, grids, Venn diagrams, Karnaugh maps, tables and tree diagrams
- the addition rule for probabilities, \( \Pr(A \cup B) = \Pr(A) + \Pr(B)–\Pr(A \cap B) \), and the relation that for mutually exclusive events \( \Pr(A \cap B) = 0 \), hence \( \Pr(A \cup B) = \Pr(A) + \Pr(B) \)
- conditional probability in terms of reduced sample space, the relations \( \Pr(A | B) = \displaystyle \frac{\Pr(A \cup B)}{\Pr(B)} \) and \( \Pr(A \cap B) = \Pr(A | B) \times \Pr(B) \)
- the law of total probability for two events \( \Pr(A) = \Pr(A | B) \Pr(B) + \Pr(A | B^{\prime}) \Pr(B^{\prime}) \)
- the relations that for pairwise independent events \( A \) and \( B \), \( \Pr(A | B) = \Pr(A), \Pr(B | A) = \Pr(B) \) and \( \Pr(A \cap B) = \Pr(A) \times \Pr (B)\) .

## Unit 2

In this area of study, students cover introductory counting principles and techniques and their application to probability and the law of total probability in the case of two events.

This area of study includes:

- addition and multiplication principles for counting
- combinations: concept of a selection and computation of \(^n C_r \) application of counting techniques to probability.

*source – VCE Mathematics Study Design*

VCE Mathematical Methods Units 1 and 2 Courses

VCE Mathematical Methods Units 1 and 2 Syllabus

## Course Content

### Probability

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