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?
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?
Combinatorics. Theoretical probability. Combining probabilities. Equally likely outcomes. Quadratic equations. Real world. Conditional probability. Tree diagrams. Experimental probability. Mathematical modelling.
Published November 2005,December 2005.
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