Arcade coin flip, win $10 or lose $4

Question

An arcade lets you flip one fair coin. If it lands heads you win 10. If it lands tails you lose 4. On average, how much do you win or lose per play?

Accepted Answer

Expected value just means "average result if you played this many, many times." You take each possible outcome, multiply it by how likely it is, and add everything up. A fair coin lands heads half the time and tails half the time. So each outcome carries a weight of one half. - Heads (probability one half): you win 10. - Tails (probability one half): you lose 4, which counts as negative four dollars. Now blend them: EV = 	frac{1}{2}(10) + 	frac{1}{2}(-4) = 5 - 2 = 3. In plain words, half the time you gain 10 (that averages out to 5 of contribution) and half the time you drop 4 (that pulls i…

Arcade coin flip, win $10 or lose $4

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