### 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?

### Two's Company

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

# Flippin' Discs

### 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

Invite children to make hypotheses about the likelihood of winning with two discs. Encourage pupils to explain their thinking and try to justify their hypotheses.

Run the simulation, once, then again and again, so that pupils are confident with what the computer is doing. Then run it 100 times and ask the pupils to comment on/explain the result. (Clicking on the horizontal panel at the bottom of the right-hand window changes the recording method from a graph to a table.)

Record the result for two discs on the board before moving onto three discs.
Invite pupils to think for a minute on their own about what will happen with three discs. Ask them to justify their conjectures with a partner and then the whole class. Use the interactivity to demonstrate what happens. Pupils can then work, perhaps in pairs, to explain the results.

You may like to stop the group part way through their work in order to talk about some effective recording methods that pairs have devised.
When ready pupils can move on to four, five, six and n discs.

### Key questions

How can you decide if a game is fair?
How many goes do you think we need to be confident of the likelihood of winning?
Are there efficient systems for recording the different possible combinations?
Can you justify any general findings you have made?

### Possible extension

How can we colour three or more discs so that we have an even chance of winning?
If we retain the current colouring of the discs, how can we change the cirteria for winning so that we have an even chance of being successful?

### Possible support

Students can use coins or coloured counters to help them list all the possible outcomes.

Teachers may want to use this recording tool to gather the results of other similar experiments that their students are carrying out:

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

A follow up problem could be Cosy Corner