The gambler
A gambler shows you a box with 5 white and 2 black marbles in it. All the marbles are identical except for their color. He invites you to draw without replacement 3 marbles from the box while you are blindfolded, and you lose if you draw a black marble.
If you lose $10 for losing the game, how much should you get paid for winning it for your mathematical expectation to be zero (i.e. to make it a fair game)?
The answer is 25.
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1 solution
First we have to calculate your probability of winning. Your chances of drawing 3 consecutive white marbles without replacement are (5/7) * (4/6) * (3/5), which simplifies to 2/7.
So if you play 7 games, on average you will lose 5, which means you will pay out 5 * 10 = $50. To make the game fair, you need to bring in $50 during your two wins, so you need to be paid (50/2) = $25 per win.