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## Confess or Not

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #8823 Fun: (2.36) Difficulty: (2.66) Category: Probability Submitted By: lesternoronha1 Corrected By: Winner4600

You and your partner in crime are both arrested and questioned separately. You are offered a chance to confess, in which you agree to testify against your partner, in exchange for all charges being dropped against you, unless he testifies against you also. Your lawyer, whom you trust, says that the evidence against both of you, if neither confesses, is scant and you could expect to take a plea and each serve 3 years. If one implicates the other, the other can expect to serve 20 years. If both implicate each other, you could each expect to serve 10 years. You assume the probability of your partner confessing is p. Your highest priority is to keep yourself out of the pokey, and your secondary motive is to keep your partner out. Specifically, you are indifferent to you serving x years and your partner serving 2x years. At what value of p are you indifferent to confessing and not confessing?

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