The mathematical study of probability originated with a series of communications between famous mathematicians Pascal and Fermat in the 1600s. They were figuring out how to solve a problem similar to this: Suppose that Heather and Tom play a game that involves a series of coin flips. They agree that if 5 heads occur before 5 tails do, then Heather wins the game. But if 5 tails occur before 5 heads do, then Tom wins the game. They each agree to pay $5 to play the game, so the winner will make a profit of $5. The first five coin tosses result in: H, T, T, H, H. Unfortunately, the game is interrupted at that point and can never be finished.
How should the $10 be distributed between Hannah and Tom?