### Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

### 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?

# The Better Choice

##### Age 14 to 16Challenge Level

Here are two games you can play. If you played both games the same number of times, in which game would you expect to win more points?

Game 1:

In every round you flip four coins and win 3 points if you get two heads and two tails

or

Game 2:

In every round you spin three 1 - 6 spinners and win 2 points for every six that appears

The interactivity below allows you to simulate both games (including versions in which it 'costs' a point to play each round).

Can you explain the result of playing each game a large number of times?