Of the subjects of a certain king, not all are truthful. In fact, if a subject is selected at random, the probability that he always tells the truth is 2/3. The probability that he never tells the truth is 1/3. The king of this country is trying to decide whom to marry. There are only two possible choices, Princess Anne and Princess Barbara. One day the king whispers to one of his subjects that his choice is Anne. This confidant hastily whispers to another person "The king has chosen ______". Which name he says depends, of course, on whether or not he is truthful. So it goes. Each person, when he hears the rumor, whispers either the name he hears or the other to someone who has not heard. Eventually, 12 people have heard the rumor. What is the probability that the 12th person has heard the truth?
2007-06-25
05:30:58
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3 answers
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asked by
aries
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