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EXERCISE 4B Question 13

"The Prosecutor's Fallacy. An accused prisoner is on trial. The defense lawyer asserts that, in the absence of further evidence, the probability that the prisoner is guilty is1 in a million. The prosecuting lawyer produces a further piece of evidence and asserts that, if the prisoner were guilty, the probability that this evidence would be obtained is999 in 1000, and if he were not guilty it would be only1 in 1000; in other words, $\displaystyle P(evidence|guilty)= 0.999$, and $\displaystyle P(evidence|not guilty)= 0.001$. Assuming that the court admits the legality of the evidence, and that both lawyers' figures are correct, what is the probability that the prisoner is guilty?"

Book Answer:0.000998

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This is one of the last few challenging and out of syllabus question in my textbooks. I am confused about ways to tackle it, whether this need Bayes' theorem, some linear solution or simply by Tree diagram.

I have been desperately listening Alexandra Stan (Million) all day, atleast I won't forget the question and you can do same, trying to find a solution to that problem and hoping someone to clearly show a solution. Thank you.

Alexandra Stan feat Carlprit - Million - Official Video - YouTube