Mathematics, 12.03.2021 15:50 calvarado12

You enter an online cooking tournament. The entry fee is $16, and the entrants make the recipes at home and vote for their favorite, which cannot be their own recipe. The top 3 finishers win money. First place wins $58, and second place wins $47. Third place wins $5. You give yourself an X chance of finishing in the top 3, and if you finish top 3, then you have an equal chance of finishing first, second, or third. What is X such that entering this tournament is a fair gamble for you. A fair gamble is one where the expected value of entering the tournament is $0.

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