Great Expectations: Probability Through Problems
Probability Articles
Why Start with Tree Diagrams?
Why the tree diagram is fundamental to studying probability - and why it should be introduced right from the start.
Probability Calculations from Tree Diagrams
Progression from natural frequencies to proportions to the multiplication rule, and hence to probability trees.
Learning Probability Through Mathematical Modelling
Moving from the particular to the general, then revisiting the particular in that light, and so generalising further.
Tree Diagrams, 2-way Tables and Venn Diagrams
Representing frequencies and probabilities diagrammatically, and using the diagrams as interpretive tools.
Independence and Dependence
When are events independent of each other? Sampling with and without replacement.
Conditional Probability Is Important for All Students!
Understanding statistics about testing for cancer or the chance that two babies in a family could die of SIDS is a crucial skill for ALL students.
Probability Resources for Teaching the Curriculum
Which Team Will Win?
A practical experiment which will introduce students to tree diagrams, and help them to understand that outcomes may not be equally likely.
The Dog Ate My Homework!
A practical experiment which uses tree diagrams to help students understand the nature of questions in conditional probability.
Who Is Cheating?
A practical experiment provides data. Moving onto expected results provides a context to establish the multiplication rule in probability, and an intuitive approach to conditional probability.
Prize Giving
What's the fairest way to choose 2 from 8 potential prize winners? How likely are you to be chosen?
Exploring the Mathematisation of Probability
The Wisdom of the Crowd
Who's closest to the correct number of sweets in a jar - an individual guess or the average of many individuals' guesses? Which average?
Capture and Recapture
How do scientists or mathematicians estimate the size of a population of wild animals?
How Confident Are You?
What proportion of people make 90% confident guesses which actually contain the correct answer?
Louis' Ice Cream Business
Should Louis go for the safer options, hoping to limit his losses, or would he be better off with a riskier strategy, focusing on maximising his profit?
To Insure or Not to Insure
Should you insure your mobile phone? It rather depends on whether you focus on the long-term pay-off or the effect of a single event.