Why do this problem?
This problem is one of a set of problems about probability and uncertainty. Intuition can often let us down when we meet probability in real life contexts; this problem has been designed to provoke discussions that challenge commonly held misconceptions such as the Gambler's Fallacy.
This printable worksheet may be useful: Do You Feel Lucky.
Hand out this worksheet (Word
) with the statements from the problem, and give everyone time to read them through and decide for themselves whether they think the advice is good or not.
Then arrange the class into pairs, and ask half the pairs to come up with arguments in favour and half to come up with arguments against following the advice. Once each pair has had time to rehearse their arguments, arrange them in groups of four with one pair arguing in favour and one pair arguing against, until they reach a consensus.
Next, bring the class together for a discussion about how they would respond to each piece of advice and the mathematics they used to justify their decisions.
Finally, ask everyone to read through the statements on their own again, to see if they have changed their original views about any of the advice. Those who have changed their minds could explain to the rest of the class which arguments they found particularly persuasive.
In the statements, it has been deliberately left ambiguous whether coins are fair or not and so on, so it may be that there is no "right" answer that can be agreed on. The important point is for learners to discuss intelligently the probability in the situations and challenge some of the popular misconceptions that arise.
Are future results affected by previous results?
Lots of advice is based on accurate statistical data - does that necessarily mean it is useful advice?
Ask learners to collect over several weeks some examples of probability misconceptions in the media, in school or at home, which could be used to create a classroom display.
The problem has been structured as a discussion task so that learners can support each other in coming to a better understanding. By allocating a view for each pair to argue, it allows those who hold these misconceptions the chance to freely explore them without fear of ridicule.