We just had a massive trial of Vingonicus, I’m sure you saw the trial on the Probastream this morning, everyone was tuned in. As you know, there were exactly two witnesses: Jacobimus and Punticious. They both have a long history of not being fully accurate. Jacobimus has a probability of 11/12 of telling the truth and Punticious has a probability of 13/14 of telling the truth. Both Jacobimus and Punticious stated that Vingonicus was guilty! We know that statistically, Vingonicus is guilty with probability 1/1300 . I’m not good at probability, but I heard you are! I was wondering if you could tell me what the probability that Vingonicus is actually guilty? (We can assume that Jacobimus and Punticious telling the truth are independent events.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 34T
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We just had a massive trial of Vingonicus, I’m sure you saw the trial on the Probastream this morning, everyone was tuned in. As you know, there were exactly two witnesses: Jacobimus and Punticious. They both have a long history of not being fully accurate. Jacobimus has a probability of 11/12 of telling the truth and Punticious has a probability of 13/14 of telling the truth. Both Jacobimus and Punticious stated that Vingonicus was guilty! We know that statistically, Vingonicus is guilty with probability 1/1300 . I’m not good at probability, but I heard you are! I was wondering if you could tell me what the probability that Vingonicus is actually guilty? (We can assume that Jacobimus and Punticious telling the truth are independent events.)

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