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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?

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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?

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Nines and Tens

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

Fixing the Odds

Age 14 to 16 Challenge Level:

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. Your friend chooses a bag at random and then chooses a ball at random from that bag. How should you distribute the balls between the two bags so as to make the probability that your friend will choose a red ball as small as possible and what will the probability be in that case?

How should you distribute the balls so as to make the probability of choosing a red ball as large as possible and what will the probability be in that case?

What happens if you have two bags, a hundred red balls and a hundred white balls?