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Nine or Ten?

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

Racing Odds

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Stop or Dare

All you need for this game is a pack of cards. While you play the game, think about strategies that will increase your chances of winning.

Can't Find a Coin?

Age 11 to 14 Challenge Level:
Imagine your teacher has set you the homework task of throwing a coin 100 times and carefully recording your results in the order that they appear. Imagine that you can't be bothered to go and find a coin - the task is just too tedious. So you decide to try to fool your teacher.

How will you go about it?

One of these students made up their homework results, which one is the most suspicious?




BACKGROUND INFORMATION

Whilst all combinations of Heads and Tails are equally likely, certain sets of results (such as all heads or alternating Heads and Tails all the way) would look rather suspicious. Why is this?
The computer here is programmed to determine whether the set of Heads and Tails falls into a suspicious category or not. Rather interestingly, if you do generate the Heads and Tails truly randomly using a coin then there is a 95% chance the the computer will know that these were generated randomly. Don't believe it? Try it out!