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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?

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A Dicey Paradox

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

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Nines and Tens

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

Tying the Rope

Stage: 3 Short Challenge Level: Challenge Level:1
There are six different possible ways of choosing two of the loose ends. Only four of these possibilities lead to the ropes being tied together, therefore the probability that Sam holds one piece of rope is $\frac{4}{6}=\frac{2}{3}$.

This problem is taken from the UKMT Mathematical Challenges.