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Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

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?

Gambling at Monte Carlo

Age 14 to 16
Challenge Level

Monte Carlo is famous not only for motor racing, but also for its large number of casinos.

A man went to Monte Carlo to try and make his fortune. Whilst he was there he had an opportunity to bet on the outcome of rolling dice. He was offered the same odds for each of the following outcomes:

  1. At least 1 six with 6 dice.
  2. At least 2 sixes with 12 dice.
  3. At least 3 sixes with 18 dice.

The man decided that these were all the same so he could choose one at random and bet on that. Was he right?