Electric Chair Problem

Suppose there is a person who has been condemned to be killed by the electric chair, the first time it is being used. There are 2 components that need to be functioning correctly for the chair to work. The chair will fail to work if component A is tampered with by a sympathetic guard. Component B includes a number of switches that can be in any one of a huge number of configurations. There is 1 configuration for which the chair does not work. The configuration should be chosen at random so it could be in the safe configuration by chance, however a guard could select the safe setting if they were friendly to the condemned person.

Question 1. Suppose that you observed that the person was not killed by the chair, and when you checked, you found that component A had not been tampered with, but component B was in the safe configuration. Would this make you more confident that the guard was sympathetic?

Question 2. Does it make any difference if you were the person who was not killed by the chair, and who found that component A had not been tampered with, but component B was in the safe configuration?

Bonus Question. Why have I placed this post in the categories religion and science?

I promise I'll explain my view of the solution in due course; as the bonus question implies, the implications are greater than the hypothetical scenario might at first suggest.

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Explore posts in the same categories: Religion, Science, Statistics

One Comment on “Electric Chair Problem”

  1. elnwood Says:

    SG = sympathetic guard saves condemned (either tampering with A, B, or both)
    SC = safe configuration
    SCR = safe configuration occuring randomly
    S = Saved

    I assume the question is whether investigating the components after someone is not executed affects the probability that the guard was sympathetic.

    In other words, P(SG|SC) > P(SG|S) ?

    P(SG|S) = P(S|SG) P(SG) / [ P(S|SG) P(SG) + P(S|SG’) (1 – P(SG)) ]
    P(S|SG) = 1 and P(S|SG’) = P(SCR) =>
    P(SG|S) = P(SG) / [ P(SG) + P(SCR) – P(SG) P(SCR) ]

    Likewise,
    P(SG|SC) = P(SC|SG) P(SG) / [P(SC|SG) P(SG) + P(SC|SG’) (1 – P(SG)) ]
    P(SC|SG’) = P(SCR) =>
    P(SG|SC) = P(SC|SG) P(SG) / [P(SC|SG) P(SG) + P(SCR) – P(SG) P(SCR) ]

    Since P(SC|SG) < or = 1, P(SG|SC) < or = P(SG|S).

    Therefore, the added information that component B was in a safe configuration ought to not make one more confident that the guard was sympathetic.


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