Unfinished Game

A Mathematics Lesson Starter

A coin is tossed repeatedly. If it comes up heads Pascal gets a point but if it comes up tails Fermat wins a point. The first person to win three points is the winner and receives the prize of £12.

Unfortunately the game had to end abruptly after three tosses of the coin. Pascal had two points and Fermat had one point. They decided to share the £12 in a ratio that matched the probability of them winning the game if it had continued.

How should they divide the £12?

 

 

 

You may be surprised at the correct answer as it is not £8 and £4!


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