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Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you guess right, you win $1/2$ of your previous amount of money and every time you lose you lose $1/2$ of your previous amount of money. What can you say about your amount of money at the end of the game?

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Hint Win corresponds to a multiple of $1.5$ and loss to $0.5$. As multiplication commutes, you end up with $(1.5\times0.5)^5=0.75^5$ times of what you start with.

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