### 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

##### Stage: 3 Challenge Level:

Here are two discs. Each disc is red on one side and green on the other.

You win if both discs show the same colour.

Complete one throw. Did you win?
Complete several throws and look at your results.

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Approximately how often do you think you would win if you completed $100$ throws?
Make a prediction and then check it by doing the experiment.

You should have won approximately half of the time. Can you explain why?

Now change the number of discs to $3$.
You win if all the discs show the same colour.

What is the probability of winning this time? Can you explain why?

What is the probability of winning with $4$ discs? Can you explain why?

Repeat for $5$ discs.

Do you notice a pattern in your results? Can you explain it?

Can you explain how to find the probability of winning for $n$ discs?