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