30.10 As every student of probability theory will know, Bayesylvania is awash wi
ID: 3350536 • Letter: 3
Question
30.10 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, travellers who ask the same question several times in an attempt to get directions to the nearest village. such traveller 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 (a) The traveller 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? (b) The traveller then asks the same native the same question a third time, and for a third time receives the answer left. What should the traveller do now? Have his chances of finding the village been altered by asking the third question?Explanation / Answer
Probability of asking a question to an Ascii= 11/16 = 0.6875
Probability of asking a question to a Bicii= 5/16 = 0.3125
Probability that a Biscii will tell the truth= 0
Probability that an Ascii will tell the truth= 0.75
a)
The individual can be an Ascii, in which case-
Probability that he told the truth= 0.75*0.75*0.6875= 0.386
The individual can be a Biscii, in which case-
Probability that he told the truth= 0*0*0.3125= 0
Total Probability= 0.386
There are 38.6% chances of reaching the village if he takes left
b)
The individual can be an Ascii, in which case-
Probability that he told the truth= 0.75*0.75*0.75*0.6875= 0.29
The individual can be a Biscii, in which case-
Probability that he told the truth= 0*0*0*0.3125= 0
Total Probability= 0.29
There are 29% chances of reaching the village if he takes left
Yes, the chances have altered as the number of times you ask the question increases there is a chance that an Ascii can lie to it
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