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9 replies to this topic

#1 brhan

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Posted 12 February 2008 - 05:30 PM

What is the expected number of times a fair die must be thrown until all scores appear at least once?
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#2 GIJeff

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Posted 12 February 2008 - 06:15 PM

What is the expected number of times a fair die must be thrown until all scores appear at least once?


Spoiler for My take

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#3 PolishNorbi

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Posted 12 February 2008 - 06:49 PM

Well appear is a tricky word, because all the numbers except for one will appear.
Spoiler for My Solution

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#4 cpotting

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Posted 12 February 2008 - 07:08 PM

It seems to me that the number of sides is irrelevant, as is whether or not you look at the only the top number, or all faces visible. The answer is always the same: infinite.

The problem asks

What is the expected number of times a fair die must be thrown until all scores appear at least once?

At the start of any tossing, there is an infinitesmal chance that one side will not turn up. For example, with a 6-sided die - assuming that we are looking at all possible faces, it is possible that "5" will not show after 1 throw (chances are 1:6). For 2 throws the chances are 1:36. For 3 throws, 1:216.. ad nauseum... For my 1,204,575,475th try, the chances are really slim, but not 0.

No matter how many times I plan to toss the die, I cannot guarantee that at least one face will not always be stubborn and be face down. So the answer is to "how many times to do you have to toss a die to see all the faces" is infinite.
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#5 cpotting

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Posted 12 February 2008 - 07:11 PM

It seems to me that the number of sides is irrelevant, as is whether or not you look at the only the top number, or all faces visible. The answer is always the same: infinite.


The exception to this would be a Mobius strip with the a number written on it! In that case the answer is 1 throw.
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#6 brhan

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Posted 12 February 2008 - 07:16 PM

Just a clarification to my question.

The die has of course 6 faces ... and when I say visible, I mean the top one.

By fair-die I mean all the numbers have equal probability of appearing on the top face.

I am asking for the expected number of throwing the die so that all the numbers (1-6) will appear (top face) at least once.
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#7 bonanova

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Posted 12 February 2008 - 08:13 PM

What is the expected number of times a fair die must be thrown until all scores appear at least once?

Spoiler for What expectation means...
Spoiler for Here's how you calculate it

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#8 Jkyle1980

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Posted 12 February 2008 - 09:04 PM

Spoiler for What expectation means...
Spoiler for Here's how you calculate it


I do see a problem here...

I haven't taken you to Vegas yet.
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#9 PolishNorbi

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Posted 12 February 2008 - 11:27 PM

Spoiler for What expectation means...
Spoiler for Here's how you calculate it


Thanks for posting that, It was exactly what i was thinking. I deleted what I was going to post when the sides were unknown and I didn't want to take the time to figure out a formula while at work.
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#10 bonanova

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Posted 12 February 2008 - 11:54 PM

Thanks for posting that, It was exactly what i was thinking. I deleted what I was going to post when the sides were unknown and I didn't want to take the time to figure out a formula while at work.

Ha! One of the benefits of being retired. B))
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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