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A man is known to speak the truth 3 out of 4 times. He throws a dice and reports a six. Find probability it is actually a six.

I tried to compute it using the probability tree (I don't wish to directly apply the formula for Bayes Theorem) only. The posts here and here explains the question but I am looking for the probability tree approach.

Also, the second part of my question is, can I solve any question using the concept of probability tree? If yes, do I need to separately learn Bayes Theorem?

Thanks for your help!!

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The tree starts with two branches, labelled "six" and "not a six" for the die throw. Can you put probabilities on those branches?

Then from each branch there are two more branches, labelled "say six" and "say not six". Put the probabilities on those four branches. Note that's a little subtle. If the die shows a five he might lie by saying "six" or choose some other number in some way. The accepted answer in one of your links discusses this.

Once you have chosed a model for how the man lies, compute the probabilities of the four end points.

Then look at those where six is reported.

For your second question, I think you can always use a tree instead of an explicit invocation of Bayes' theorem.

I would recommend contingency tables: Applied Probability- Bayes theorem

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