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?
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?
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. Your friend chooses a bag at random and then chooses a
ball at random from that bag. How should you distribute the balls
between the two bags so as to make the probability that your friend
will choose a red ball as small as possible and what will the
probability be in that case?
How should you distribute the balls so as to make the
probability of choosing a red ball as large as possible and what
will the probability be in that case?
What happens if you have two bags, a hundred red balls and a
hundred white balls?