1 An absentminded professor does not remember which of his 12 keys will open his office door....

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1 An absentminded professor does not remember which of his 12 keys will open his office door. If he tries them at random and with replacement:

(a) On average, how many keys should he try before his door opens?

(b) What is the probability that he opens his office door after only three tries?

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