Question about who tells the truth.

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SUMMARY

The discussion centers on calculating the probability that person C lied based on the truth-telling probabilities of persons A and B. It establishes that if A and B tell the truth with probability p, the probability that C lied is given by the formula p² + (1-p)². Additionally, a related probability problem involving two coins is presented, asking for the probability that both coins show heads given that one coin shows heads and the truth-telling probability p of the friend. This highlights the application of probability theory in assessing information transmission among multiple parties.

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Alexsandro
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Interesting question:

" A says that B told him that C lied ".

If each of these person tells the truth with probability p, what is the probability that C lied ?
 
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It is clear that A and B transmit information rightly if they tells the truth simultaneously or if they tells the false simultaneously. Therefore the probability that C lied is equal to

p^2+(1-p)^2.
 
Hmm,
on a somewhat similar note,
Your friend tosses two coins simultaneously far away hidden from you. Then he shouts out loud to you that one of the coins shows head.
1. What is the probability that both the coins show head?
2. If your friend utters truth with a probability p, then what is the probability that both the coins are head?

-- AI
P.S -> I am sure this is not a digression from the original question, just an example that i hope should give some idea on the original question.
 

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