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Topic: Drunken Rave in a Hotel (Read 833 times) |
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abc123
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Drunken Rave in a Hotel
« on: Mar 2nd, 2007, 5:02pm » |
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We have 100 guests, each with a room and a corresponding key. Adding up to 100 rooms, and 100 keys. One night all the guests go to a local night club, so they have to each leave there key at the reception. But get absolutely wasted, and therefore forgetting their room numbers. When they go back to the hotel they each randomly take a key from the reception box and go back to the room from which the keys belongs to.
What is the probability at least one guest will go to their original room?
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| « Last Edit: Mar 5th, 2007, 3:53pm by abc123 » |
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Whiskey Tango Foxtrot
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Re: Drunken Rave in a Hotel
« Reply #1 on: Mar 2nd, 2007, 5:16pm » |
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1/10000
If each time a guest tries a room and fails, he remembers the room number and moves on to a different, random room, on average how many rooms will each person try before they enter their own?
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| « Last Edit: Mar 2nd, 2007, 5:20pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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ThudnBlunder
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Re: Drunken Rave in a Hotel
« Reply #2 on: Mar 2nd, 2007, 5:33pm » |
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on Mar 2nd, 2007, 5:16pm, Whiskey Tango Foxtrot wrote:
Are you deranged? 
Should be a little under 1 - (1/e)
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| « Last Edit: Mar 5th, 2007, 5:50pm by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Whiskey Tango Foxtrot
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Re: Drunken Rave in a Hotel
« Reply #3 on: Mar 2nd, 2007, 5:47pm » |
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on Mar 2nd, 2007, 5:33pm, THUDandBLUNDER wrote:
Whoops.  I read this
on Mar 2nd, 2007, 5:02pm, abc123 wrote:
What is the probability at least one guest will go to their correct room? |
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as something entirely different.
The fact that I'm holding a White Russian (or Caucasian to some of you) in my hand right now might help to explain some of my confusion. All that talk about people getting absolutely wasted and forgetting wore off on me. 
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| « Last Edit: Mar 2nd, 2007, 5:48pm by Whiskey Tango Foxtrot » |
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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abc123
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Re: Drunken Rave in a Hotel
« Reply #4 on: Mar 5th, 2007, 3:56pm » |
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Sorry i got it a bit wrong, or you got slightly confused ^_^ What i meant was each guest took a random key from the box, then went to that room. So what is the probability that at least one guest found their original key. :x :]
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Random Lack of Squiggily Lines
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Re: Drunken Rave in a Hotel
« Reply #5 on: Mar 5th, 2007, 5:04pm » |
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1 in a 100
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You can only believe i what you can prove, and since you have nothing proven to cmpare to, you can believe in nothing.
I have ~50 posts to hack a "R" into a "D". Which one?
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ThudnBlunder
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Re: Drunken Rave in a Hotel
« Reply #6 on: Mar 5th, 2007, 5:54pm » |
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on Mar 5th, 2007, 3:56pm, abc123 wrote:| So what is the probability that at least one guest found their original key. :x :] |
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It is 1 - Probability that nobody chose their own key
This equals approximately 1 - 0.368 = 0.632
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| « Last Edit: Mar 6th, 2007, 2:21am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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Random Lack of Squiggily Lines
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Re: Drunken Rave in a Hotel
« Reply #7 on: Mar 15th, 2007, 11:17am » |
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actually 1 in 14, because 86 of them dont make it back, like you said , the got wasted. in fact i thought i saw 1 of them in a dumpster in toronto
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You can only believe i what you can prove, and since you have nothing proven to cmpare to, you can believe in nothing.
I have ~50 posts to hack a "R" into a "D". Which one?
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Aryabhatta
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Re: Drunken Rave in a Hotel
« Reply #8 on: Mar 15th, 2007, 1:25pm » |
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on Mar 15th, 2007, 11:17am, tiber13 wrote:| actually 1 in 14, because 86 of them dont make it back, like you said , the got wasted. in fact i thought i saw 1 of them in a dumpster in toronto |
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This is actually an interesting scenario.
Each of the remaining 14 guys picks a key (from 1 to 100) at random. What are the chances that some guys picks his own key.
I don't think that it would be 1/14.
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Padfoot
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Re: Drunken Rave in a Hotel
« Reply #9 on: Mar 15th, 2007, 2:43pm » |
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on Mar 15th, 2007, 1:25pm, Aryabhatta wrote:
Each of the remaining 14 guys picks a key (from 1 to 100) at random. What are the chances that some guys picks his own key.
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14/100 ?
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Aryabhatta
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Re: Drunken Rave in a Hotel
« Reply #10 on: Mar 15th, 2007, 4:24pm » |
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on Mar 15th, 2007, 2:43pm, Padfoot wrote:
Don't know.
Maybe I should have stated it better:
"What are the chances that at least one of the 14 picks his own room key?"
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