As every student of probability theory will know, Bayesylvania is awash with natives, not all of whom can be trusted to tell the truth, and lost, and apparently somewhat deaf, travelers who ask the same question several times in an attempt to get directions to the nearest village.
One such traveler finds himself at a T-junction in an area populated by the Asciis and Bisciis in the ratio 11 to 5. As is well known, the Biscii always lie, but the Ascii tell the truth three quarters of the time, giving independent answers to all questions, even to immediately repeated ones.
1. The traveler asks one particular native twice whether he should go to the left or to the right to reach the local village. Each time he is told "left". Should he take this advice, and, if he does, what are his chances of reaching the village?
2. The traveler then asks the same native the same question a third time, and for a third time receives the answer "left". What should the traveler do now? Have his chances of finding the village been altered by asking the third question?