Why do this problem?
offers an opportunity to explore and discuss two types of probability: experimental and theoretical. The simulation generates lots of experimental data quickly, freeing time to focus on predictions, analysis and justifications.
Demonstrate the interactivity with three or four single shakes.
"Estimate the probability of winning." Allow students some thinking and discussion time in pairs before bringing them together to state their initial conjectures.
Students may find these sheets
Record their conjectures on the board and then run the interactivity for a hundred shakes.
Ask the students to return to their pairs and use the extra evidence to refine and justify their conjectures.
Run the interactivity for several hundred shakes to test the new hypotheses.
Discuss the efficiency of alternative methods of recording the different combinations systematically.
Are there efficient systems for recording the different possible combinations?
What counts as a different outcome?
If the red balls are in the same position but a blue and yellow ball swap places, does that count as a different outcome?
How can we make this game fair?
A follow-up problem could be Two's Company
A less demanding alternative problem is Flippin' Discs
Teachers may want to use this recording tool to gather the results of other similar experiments that their students are carrying out:
Full Screen Version
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.
You can view and print the RecordSheet.pdf
here (pdf 311 kB).