M1Maths

Modules - 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.

Modules:   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.

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

Modules:   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.

Compound Events

• addition and multiplication rules

Two-way Tables

• using two-way tables to determine probabilities

Venn Diagrams

• using Venn diagrams to determine numbers and probabilities

Modules:   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.

Tree Diagrams

• using tree diagrams to determine probabilities

Modules:   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.

Complex Probabilities

• using the addition and multiplication rules in combination

Modules:   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.

Sets

• set terminology and notation

Conditional Probability

• conditional probability

Discrete Random Variables

• discrete random variables

• discrete probability distributions

• expected value and variation

Binomial Distributions

• binomial probabilities

Continuous Random Variables

• probability density functions

• expected value, quantiles and spread

• cumulative distribution functions

• mean and variance of aX + b

Normal Distributions

• finding probabilities from values

• finding values from probabilities

• z-scores

Confidence Intervals

• confidence intervals for proportions

• confidence intervals for means

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