A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?
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?
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?
The number of throws to get a million pounds would be at least 20 since
2^20 is 1,048,576.
This would require throwing at least 19 tails
sequentially, which has a probability of 1/ 2^19 or 1/524,288, or
The amount you should pay to play the game is less than or equal to the
expected value of the winnings.
After the first turn the expected winnings
are 1/2*2 = 1 pound.
After two turns the expected winnings are 1 + 1/4*4 =