Probability that C lied given A reports B's claim

[Alexsandro]

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 ?

 

[nworm]

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.

 

[TenaliRaman]

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.