. A woman has N keys on her key ring. Frantic to open the door, she selects a key at random and tries it. Each key is no more likely to be selected than any other and only one of the keys will open the door. If the door opens, she shoves the children in while trying not to let in any birds. If not, she discards the key and randomly and independently selects another key and tries again. Find the mean and variance of the number of trials required to open the door. Note: if the door opened on the rst attempt, one trial was required, etc.

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