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Win or Lose?

A gambler bets half the money in his pocket on the toss of a coin, winning an equal amount for a head and losing his money if the result is a tail. After 2n plays he has won exactly n times. Has he more money than he started with?

Fixing the Odds

You have two bags, four red balls and four white balls. You must put all the balls in the bags although you are allowed to have one bag empty. How should you distribute the balls between the two bags so as to make the probability of choosing a red ball as small as possible and what will the probability be in that case?

Scratch Cards

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

Coin Lines

Age 14 to 16
Challenge Level

  • A coin is randomly tossed onto a set of parallel lines. If the line separation matches the diameter of the coin, what is the chance that the coin touches a line?
  • And what if the line separation is different ? Double ? Half ?

  • If the lines become concentric circles and the gap between the lines doubles, what is the chance now that the coin touches a line?

An answer might be guessed at but the problem is really about justifying that answer.

Do you have a way of visualising it and could you convince a friend?

If you succeed with that it should be an easy next step to generalise for a coin of any size.