Why do this problem:

Probability often forces us to be particularly careful with our justification of answers. This problem has a simple enough numerical answer but the visualisation to support it must be carefully considered.

Possible approach :

This problem might make a good poster, displayed somewhere it will catch students' attention to promote discussion.

The extent to which students need some practical activity will depend on how accustomed they are with visualisation tasks.

Key questions :

• What do you think the answer might be?
• Do you have a way of looking at this situation so that you are sure your answer is right?

Possible extension :

• Research the problem context called Buffon's Needle

Possible support :

For students who cannot access this problem directly or theoretically the following activities may be helpful :

• Draw some parallel lines at equal intervals and vary the size of that interval. Include in particular double and treble the coin diameter. Keep a tally of results.

• Draw the concentric circles and collect experimental data.