### 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

Game 1:

Imagine the four coins appear in a line, for example H T H H.
How many arrangements like this are there?
In how many cases would you win 3 points?

If you played the game a specified number of times (e.g. 16 or 32 or 64 times), how many points would you expect to win?

Game 2:

You could get three sixes.
If you got three sixes, how many points would you win?
How often might you expect that to happen?

You could get two sixes.
If you got two sixes, how many points would you win?
How often might you expect that to happen?

What else could you get?

If you played the game a specified number of times (e.g. 216), how many points would you expect to win?