Two bags contain different numbers of red and blue balls. A ball is
removed from one of the bags. The ball is blue. What is the
probability that it was removed from bag A?
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?
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?
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
The man decided that as these were all the same, he would choose
one at random and bet on that. Was he right ?