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Solutions: Bayes Plays Cluedo – in a nutshell.

March 21, 2019

Solutions to Bayes Plays Cluedo – in a nutshell.

  1. There are five suspects, each of whom is equally likely of being guilty. So the prior probability of guilt for each is 20 per cent (0.2).
  2. There are now four suspects left, each of whom is equally likely to be guilty. So the new probability that each of the remaining suspects is guilty is 25 per cent (0.25).
  3. A new clue means that the probability of guilt we assign to Colonel Mustard rises to 40 per cent, so the probability we should assign to each of the other three suspects is 20 per cent each (60% divided by three).
  4. The 20 per cent probability of guilt we assigned to Mrs. Peacock should now be distributed to the remaining suspects in proportion to the prior probability of guilt before Mrs. Peacock was eliminated. These were 40% (Mustard), 20% (Scarlett) and 20% (Plum). So the 20% should be distributed in a 4-2-2 proportion, i.e. 10% to Mustard, 5% to Scarlett and 5% to Plum. The posterior probability for each becomes 50% (Colonel Mustard), 25% (Miss Scarlett), 25% (Professor Plum).

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