Card game: conditional probability

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This task assesses how well students understand calculating conditional probability.

The task features a game of ‘higher or lower’ being played with cards numbered 1 to 10. Several turns in a game are shown and students must write the probability that the next card is either higher or lower.

This task would be particularly helpful as a way of introducing conditional probability, perhaps ahead of working on tree diagrams.

The final question shows the numbers 3, 10, 4, 7, and 1 as revealed. The statement is then made that: ‘when the sixth card is turned the probability that the following card is higher is the same as the probability that it is lower.’ The task is to work out what the sixth card must be.

This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. A full rubric is given for the task, together with examples of student work and suggestions for helping students overcome misconceptions. Further information on the collection is given here.

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