Charity coin toss, receive $7 or donate $5

Question

At a charity booth you flip one fair coin. Heads means the booth hands you 7. Tails means you donate 5. On average, how much do you come away with per flip?

Accepted Answer

Expected value is the average result over many plays: each outcome times its chance, all added together. A fair coin gives heads half the time and tails half the time, so each side gets a weight of one half. - Heads (probability one half): you gain 7. - Tails (probability one half): you give 5, which is negative five dollars for you. Combine them: EV = 	frac{1}{2}(7) + 	frac{1}{2}(-5) = 3.5 - 2.5 = 1. So the 7 side contributes an average of 3.50 and the donation side pulls back 2.50, leaving a net average gain of 1 in your pocket per flip. Any single flip is either plus 7 or minus 5, never …

Charity coin toss, receive $7 or donate $5

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