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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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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?

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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?

Do You Feel Lucky?

Stage: 3 and 4 Challenge Level: Challenge Level:1
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?