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Recommended prior knowledge
All of Core and particularly Core 9. Only those parts of the learning objectives or notes and exemplars not included in the core units are itemised, so this document should be read alongside the Core document.
Context
There are 2 Core statistics units and this is the first of two Extended statistics units. Once the Core 9 and the other prior experience for Core 9 is completed this unit can be slotted in at any point. It is probably best taught as a whole as there is a flow to the content.
Outline
The unit extends the knowledge of Core 9 so be aware that examination questions that relate to aspects of Core 9 may have a greater degree of challenge as they combine with other areas of mathematics. This unit covers combined probabilities.
Syllabus ref Learning objectives Suggested teaching activities Learning resources
9.4
CCSS:
S-CP1
S-CP2
S-CP7
Combining events: the addition rule P( A or
B ) = P( A ) + P( B ) – P( A and B ) the multiplication rule
P( A and B ) = P( A ) ×
P( B ).
General guidance
This is easiest to model on tree diagrams where the ends of branches are added and the route along a branch is multiplied. The statement read along a string of branches leads to use of ‘of’ that therefore and understanding of why we multiply along the branches. Checking the sub branch additions to 1 also confirms when to add (and check for errors particularly in the case where items are removed and not returned for the second go)..
Teaching activities
Setting up a tree diagram for the game below is interesting and has a surprising result. Player A always starts and throws a dice. If the dice lands on 1 player 1 wins. If player A does not win player B has a go and wins if they roll a 2 or a 3, if player B does not win then player three has a go and wins if a 4, 5 or 6 is rolled. If C doesn’t win return to player A and continue.
Work out the probabilities of each player winning. Who will be the most likely winner and the likely length of the game. (Theoretical probabilities of each player winning are P(A)= 3/13. P(B)= 5/13 and P(C) = 5/13 The task could continue by changing the rules to see the effect of different rules) (This is www.bbc.co.uk/schools/gcsebitesize/math s/data/probabilityhirev1.shtml
www.shodor.org/interactivate/lessons/Con ditionalProb/ nrich.maths.org/920
Past Paper 41 June 2011 Q2
(syllabus 0580)
Past Paper 43 June 2011 Q7
(syllabus 0580) v1 2Y01 Cambridge IGCSE Mathematics (US) 0444 1

Syllabus ref Learning objectives Suggested teaching activities adapted from an EDEXCEL coursework task for GCSE).
Learning resources v1 2Y01 Cambridge IGCSE Mathematics (US) 0444 2