A gambler throws a die and tells the score. He tells truth 3/4 of the times that he speaks and randomly lies 1/4 of the times that he speaks. If he says it is a six, what is the probability that he actually got a six?

Well, we could do the whole conditional probability thing, but it is really not required here. Assuming the die is fair and his lies are completely random (with respect to the number he has really rolled when he lies and the number that he claims to have), then any statement he makes has a 3/4 probability of being true. In particular, if he says he has rolled a 6, then the probability that he really has is 3/4.