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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 as these were all the same, he would choose one at random and bet on that. Was he right ?