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 have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two bags
so as to make the probability of choosing a red ball as small as
possible and what will the probability be in that case?
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. He repeats this many times, each time betting half the total money he has. After $2n$ plays he has won exactly $n$ times. Has he more money, the same amount or less money than he started with?