Representing conditional probabilities 2

This is a concept development lesson that is designed to assess how well students understand:

• When conditional probabilities are equal for particular situations
• Representing events as a subset of a sample space using tables and tree diagrams
• Modelling using algebra

This lesson can be used as an extension to ‘Representing conditional probabilities 1’ or by itself.

A game about taking black and white balls from a bag is to be devised. The player wins if the two balls the same colour and loses if the balls are different colours. A series of eight scenarios are shown where varying numbers of black balls are placed in a bag. The task each time is to work out how many white balls are needed to make the game fair.

The final question generalises the situation, with m black balls and n white balls being placed in a bag. Students must arrive at an algebraic connection between m and n in the situation where the game is fair.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.