A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
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?
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags (it is not known from which bag). The marble is blue. What is the probability that it was removed from bag A?