MHB Solving "Who Dunnit": Calculating Probability of Joshua McCoy's Involvement

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The discussion centers on calculating the probability of Joshua McCoy's involvement in hanging two dead rats on Zacariah Hatfield's porch, following a series of events involving a moonshine still. Event A involves Zacariah publicly accusing Joshua of moonshining, while Event B is his report to the sheriff after finding the first dead rat. Events C1 and C2 represent the occurrences of the dead rats appearing on Zacariah's porch. The sheriff needs to determine whether these acts were random or the result of Joshua's retaliation, which requires understanding the underlying probabilities. The thread seeks assistance in quantifying these probabilities to solve the "Who Dunnit" mystery.
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I posted my original "Who Dunnit" on September 6 and got 190 Views amd 0 Responses. I need help solving "Who Dunnit"."Who Dunnit" is a symbolic story that represents a series of events that actually occurred. Two distinct events, A and B, occurred. Events A and B were about a certain person. Events C1 occurred after Event A and C2 occurred after Event B. C1 and C2 were the same action just occurring at two different times. The question in "Who Dunnit" is how do you calculate the probability that the certain person whom events A and B were about committed events C1 and C2. All responses will be greatly appreciated.

Here is "Who Dunnit" :

The Hatfields and McCoys have been feuding longer than anyone can remember. One day while Zacariah Hatfield was out hunting squirrels in the forest, he runs across an active moonshine still. Zachariah is convinced that Joshua McCoy is making moonshine with the still and Zachariah writes a letter to the editor of the local newspaper publicly announcing he found a still in the forest that he alleges belongs to Joshua McCoy. Five days after Zachariah's letter appears in the newspaper, Zachariah discovers a dead rat hanging from the ceiling of his front porch. Zachariah is convinced that Joshua McCoy hung the dead rat on his front porch and reports the incident to the local sheriff accusing Joshua McCoy. Three days after Zachariah talks with the sheriff, he discovers another dead rat hanging from the ceiling of his front porch.

Before the sheriff can confront Joshua McCoy he needs to determine what are the chances both dead rats were a random act by the local hooligans. Can anyone help out the sheriff?

Event A is Zachariah Hatfield writes a letter to the editor of the local newspaper publicly announcing he found a still in the forest that he alleges belongs to Joshua McCoy. Event A is about the certain person, Joshua McCoy.

Event C1 is a dead rat is hung on Zachariah Hatfield's front porch.

Event B is Zachariah Hatfield reports the incident to the local sheriff accusing Joshua McCoy because he is convinced that Joshua McCoy hung the rat on his front porch because Zachariah "ratted" on Joshua. Event B is about the certain person, Joshua McCoy.

Event C2 is a second dead rat is hung on Zachariah Hatfield's front porch.

The sheriff needs to calculate the probability that Joshua McCoy hung both dead rats on Zachariah Hatfield's front porch.
 
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It is impossible to answer this without knowing some basic numerical probabilities that the person will or will not do these things.
 
There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...

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