Gambling at Monte Carlo

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.

Marbles and Bags

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?

Coin Tossing Games

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?

Chances Are

Stage: 4 Challenge Level:

We are often blasted with opportunities to "take a chance" to try to win an attractive prize for what seems like very little money and with an apparently good chance of striking lucky (how wrong can you be?). Below are some examples of opportunities to win a holiday for two at a well known resort. It will only cost you the price of a bottle of water to take part.

If you were extravagant enough to "try your luck", which of the following offers the best chance of you winning and how do you know?

I think I would prefer the water - especially on a hot summer's day! But you might not agree.