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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?

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.

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:

Some people offer advice on how to win at games of chance, or how to influence probability in your favour for an easier, happier life. For each statement below, decide whether you think it is good advice, and use your mathematical understanding to justify your decisions.
Lottery advice: (for information on how lotteries work, click here)
Roughly equal numbers of odd and even are drawn most weeks, so you should pick a good mixture of odds and evens.

Choose six numbers with a total between 100 and 200, because the total is rarely outside this range.
Never choose six numbers all from the same group - for example, all single digits, all multiples of five, all with the same last digit... 

Always pick some higher numbers from the 30s and 40s.
Coin Flipping:
If tails has come up on the last 9 occasions then it's a good idea to call tails again. 
Winning at Roulette:
If red has come up lots of times in a row, you should bet on black next.
Snakes on a plane:
When you're flying, always take a pet snake with you in your hand luggage. The probability of there being TWO snakes on the plane is almost zero, so you will be safe from snake attack.
Staying dry at the cricket match:
Follow the example of the famous mathematician Hardy and take an umbrella with you to cricket matches. If you forget your umbrella it is more likely to rain, so if you remember to take it with you it is more likely to be sunny all day.
Send us your thoughts on these pieces of advice, as well as any other examples you can find of people giving unhelpful advice based on statistics and probability.