Pat takes part in a quiz show with multiple choice questions. There are three possible answers to each question. The probability that she knows the answer to a question is p. If Pat does not know the answer to a particular question, she gives an answer at random. If she answered the first question correctly, the probability that she knew the answer is

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3p P (b) p (c) 1+2p P+1/3 (d) P P+ 1/2 3p 22