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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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Nine or Ten?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Do You Feel Lucky?

Age 11 to 14 Challenge Level:
How lotteries work:
In the UK, lottery players choose six different numbers between 1 and 49. When the lottery draw takes place, 49 coloured balls numbered from 1 to 49 are placed in a machine and spun round, and then six balls are released at random. Any player who chose the six numbers picked by the machine wins the jackpot prize. Other lotteries use similar systems, perhaps with more or fewer numbers to choose from.
Can you think of examples where future events are influenced by past events?
Can you think of examples where future events are independent of past events?