1.2 No 36

#87
by rgwfwerfwqedqwed - opened

😃: Four friends have been identified as suspects for an unauthorized access into a computer system. They have made
statements to the investigating authorities. Alice said
“Carlos did it.” John said “I did not do it.” Carlos said
“Diana did it.” Diana said “Carlos lied when he said that
I did it.”
a) If the authorities also know that exactly one of the
four suspects is telling the truth, who did it? Explain
your reasoning.
b) If the authorities also know that exactly one is lying,
who did it? Explain your reasoning
🤖: Let's analyze each statement:

a) If the authorities know that exactly one of the four suspects is telling the truth, we can use Bayes' theorem to update our belief in their guilt or innocence based on the statements they make. Here are the possible combinations and their probabilities:

  1. Alice says Carlos did it (Alice accuses Carlos): P(Carlos guilty | Alice's statement) = 0.75 (based on the fact that only one person could have accessed the system without authorization).
  2. John says I didn't do it (John denies involvement): P(John guilty | his statement) = 0.25 (since John has denied any involvement, which suggests he might be telling the truth).
  3. Carlos says Diana did it (Carlos blames Diana): P(Diana guilty | Carlos' statement) = 0.5 (since Carlos implicates Diana, but this doesn't necessarily mean she's guilty).
  4. Diana says Carlos lied about her (Diana dis...

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