Spoiler Inside: Solution to Puzzle | SelectShow |
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The way to solve a problem like this is by calculating the expected value. Take the probability of each possibility and multiply by the payout/cost. Add all such. If the result is positive, it pays to take the bet.
In the first scenario, the expected value is 1/8 × $8 + 3/8 × $12 + 3/8 × $18 + 1/8 × $27 = $15.625 then minus the $16 paid to give $-0.375. Since the expected value is negative, do not go for this bet. In the second scenario, the expected value has more detail and it works out to $18.546875 minus the $20 paid to give $-1.453125. Since the expected value is negative, do not go for this bet. In the third scenario, the expected value works out to $12.703125 minus the $12 paid to give $0.703125. Since the expected value is positive, go for this bet. |