# Probability

**AS level Probability**

- Understand and use mutually exclusive and independent events when calculating probabilities
- Link to discrete and continuous distributions

**A Level Probability**

- Understand and use conditional probability, including the use of tree diagrams, Venn diagrams, two-way tables
- Understand and use the conditional probability formula
- Modelling with probability, including critiquing assumptions made and the likely effect of more realistic assumptions

### Probability: Random Independence

This activity involves the quest to show whether two events are independent. Students are required to use a Venn diagram and to apply logic to find all possible combinations of values within the diagram and thus calculate the probability of event A and event B being independent events. The answer provides a full explanation of the solution.

### Probability: Biased Dice Independence

Students are presented with a normal six sided dice students and are asked to show that the probability of two events 'the score is odd' and 'the score is prime' are not independent.

Students are then given conditions for the probabilities of the scores on a biased dice and are challenged to discover if it is now possible for the same two events to be independent.

The answer sheet provides a full explanation of the solution.

### Venn Diagrams

This resource contains an interactive spreadsheet by Michael Bawtree.

It allows students to explore mutually exclusive events and conditional probability using Venn diagrams.

The conditional probability formula is defined and used in order to answer questions based on information displayed in Venn Diagrams.

### Probability: the Colin and Phil Problem

In this Powerpoint activity Colin and Phil take it in turns to roll a dice. The winner is the first to throw a six. Students are asked to investigate conditional probability to find the probability of each player winning and hence determine whether the game is fair. The presentation provides a complete solution before continuing to pose a series of related challenges. The solution is explained using tree diagrams.

### Exploring Statistics

This resource contains a series of short problems and longer investigations to stimulate discussion of statistics and to provide a deeper understanding of the statistics topics found in Advanced level courses. There are a number of probability investigations including those which use probability models.