A drunk has five keys on his key chain, and only one will open the front door of his house. He tries each key until he finds the right one. Assume that he is so drunk that he may repeat the wrong key any number of times. On average how many trials he will make to open the front lock of his house.
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2A more interesting version of the problem: [Drunk man with a set of keys.](https://math.stackexchange.com/q/2044007/318073). – Vepir Apr 12 '20 at 13:54

Does this answer your question? [6 keys and a door( probabilities)](https://math.stackexchange.com/questions/781073/6keysandadoorprobabilities) or this? [What's the Probability of a drunk man open a door with n possible keys?](https://math.stackexchange.com/q/2760572/318073). It appears the same question was asked multiple times on the site already... – Vepir Apr 12 '20 at 14:01

Does this answer your question? [5 keys and lock](https://math.stackexchange.com/questions/3621864/5keysandlock) – awkward Apr 12 '20 at 14:50
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Hint:
Consider Bernoulli trials with $p=1/5$.
Then you are looking for the expected No. of trials till reaching the first success.
That' a Geometric distribution
G Cab
 33,333
 3
 19
 60