### 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 Bet

##### Stage: 4 Challenge Level:
First the coins :

Imagine the four coins in a line, for example T H H H.
How many arrangements like this are there?
How many would win the $£3$?

If you played the game a specified number of times how much do you think you might have as profit or loss?
How much would that be on average per game?

Now the dice :

You could get $3$ sixes, what else could you get?
If you got $3$ sixes, how much would you win?
How often might you expect that to happen?
What about an overall expected profit or loss in the long run?