Sociable Cards
Why do this problem?
This problem is one of a set of problems about probability and uncertainty. Intuition can often let us down when working on probability; these problems have been designed to provoke discussions that challenge commonly-held misconceptions. Read more in this article.
Possible approach
Arrange learners in groups of 4, with a pack of cards and some counters for each group. Ask them to remove the Jacks, Queens and Kings, and then shuffle the remaining cards. Explain how to set up the 'snake' and then ask them to put a different counter on each of the first four cards. Once they have chosen a counter each, get them to see how far they can each go before falling off the end.
| All counters on the same card | |
| Three counters on the same card | |
| Two pairs of counters on two cards | |
| Two counters on the same card | |
| All counters on different cards |
Finally, allow some time for learners to work on the challenge of finding a snake where all four (and then five) counters end up on different cards.
Key questions
Where did your counters end up?
Possible support
The initial task should be accessible to all. When planning a way to use the activity as a fundraiser, less confident learners could be encouraged to restrict the winning options. For example, they could explore pricing structures for a game that only pays out when all participants land on different cards.
Possible extension
Retiring to Paradise provides a different context for considering the importance of spread as well as average when working with data.
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