### The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

### Master Minding

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

### Flippin' Discs

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

# Two's Company

### Why do this problem?

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.

### Possible approach

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 fiind these sheets useful.
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.

### Key questions

Are there efficient systems for recording the different possible combinations?
What counts as a different outcome?
If the yellow and red marbles are in the same position but the blue marbles swap places, does that count as a different outcome?

### Possible extension

How can we make this game fair?
A follow-up problem could be The Better Bet

### Possible support

This problem could be tackled as a follow-up to Cosy Corner

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
This text is usually replaced by the Flash movie.

You can view and print the RecordSheet.pdf  here (311 kB).