Home                   Modules                     Extras for Students                      Extras for Teachers M1Maths

# Probability

Level 1       Level 2       Level 3       Level 4       . . . . .       Level 6

Level 1 is Years 5-7, Level 6 Years 11-12.

Many textbooks treat probability very poorly. One common error is to define probability as the number of outcomes in the event divided by the number of outcomes in the sample space. This depends on the probability of all outcomes in the sample space being equal, something often not mentioned. The definition is also circular in that the definition of probability depends on the idea that the probabilities of the outcomes are equal and thus on knowing what probability means. A more appropriate definition of probability is the fraction of times that something will happen in the long run and this is the way it is introduced here.

Probabilities can be determined using data, symmetry or guesswork, guesswork being required for untestable and unrepeatable events like finding there is an afterlife if you die. By the end of the course, student will be able to do all the usual calculations, but will have a more solidly grounded concept of what it is all about.

 P1:     Probability - Level 1 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 1 modules.
P1-1 pdf     docx

## Probability

• the meaning of probability
• finding approximate probabilities using data (from experiment and pre-existing) and understanding the reliability of the approximations
• estimating probabilities by guesswork
• finding exact probability using indifference, deciding when it applies
• calculating expected frequency
8 h N1-3

 P2:     Probability - Level 2 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 2 modules.
P2-1 pdf     docx

## Compound Events

5 h
P2-2 pdf     docx

## Two-way Tables

• using two-way tables to determine probabilities
1 h P2-1
P2-3 pdf     docx

## Venn Diagrams

• using Venn diagrams to determine numbers and probabilities
3 h

 P3:     Probability - Level 3 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 3 modules.
P3-1 pdf     docx

## Tree Diagrams

• using tree diagrams to determine probabilities
3 h

 P4:     Probability - Level 4 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 4 modules.
P4-1 pdf     docx

## Complex Probabilities

• using the addition and multiplication rules in combination
4 h

 P6:     Probability - Level 6 Click the link in the second column for the required format. Word documents need to be downloaded and opened in Word to display properly. The second last column is the estimated time required to work through the module; the last column is the pre-requisite Level 6 modules.
P6-1 pdf     docx

## Sets

• set terminology and notation
2 h
P6-2 pdf     docx

## Conditional Probability

• conditional probability
3 h
P6-3 pdf     docx

## Discrete Random Variables

• discrete random variables
• discrete probability distributions
• expected value and variation
5 h
P6-4 pdf     docx

## Binomial Distributions

• binomial probabilities
5 h P6-3 A6-1
P6-5 pdf     docx

## Continuous Random Variables

• probability density functions
• expected value, quantiles and spread
• cumulative distribution functions
• mean and variance of aX + b
5 h P6-3 C6-10
P6-6 pdf     docx

## Normal Distributions

• finding probabilities from values
• finding values from probabilities
• z-scores
5 h P6-5
P6-7 pdf     docx

## Confidence Intervals for Proportions

• confidence intervals for proportions
4 h P6-4
P6-8 pdf     docx

## Confidence Intervals for Means

• confidence intervals for means
3 h P6-7

 Background image: https://pixabay.com/illustrations/beach-background-sea-ocean-3892386/ (cropped) (Creative Commons licence)