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Math Help - Conditional Probability

  1. #1
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    Conditional Probability

    The book says that prospective philosophy students at Cambridge used to be asked this question:

    "Four witnesses, A, B, C, and D, at a trial each speak the truth with probability 1/3 independently of each other. In their testimonies, A claimed that B denied that C declared that D lied. What is the conditional probability that D told the truth?"

    I'm stumped on this one. Any idea where to start?
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  2. #2
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    i suspect many people got into cambridge who happened to have watched the right episode of doctor who ......

    You may find it easier to think through the case with 2 people (something similar was featured in doctor who about 30 years ago, to explain the reference).

    hint:
    what happens if an even number of them are lying?
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