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| Sep-01-13 | | Marmot PFL: <kellmano> One way to look at this problem is that 99 other people distributed randomly over 20 groups works out to 4.95 per group (round it to 5). So the most probable answer would be 5 other people. If that's wrong, so be it, but at least it doesn't take 3 lines of equations and a calculator. |
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| Sep-01-13 | | kellmano: <mamrmot> that was my intention, but it turns that I had picked values that meant the modal amount was 4 extra so 5 in total. According to <al wazir> and <tiggler>. The distribution is not symmetrical about 5 extras (or 4.95). There can be 11 a group, but not minus 1, to illustrate. |
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Sep-01-13
 | | Sneaky: <100 people are given a random number between 1 and 20. Each group of people with like numbers forms a group. What size group do you expect to be in?> This question and its subsequent discussion is confusing me to no end. So I play this game and the random number guy gives me number 17. So then I watch 99 more people get assigned numbers. I should expect 99/20 of them to get a 17 as well, and I'm already in my group, so 1 + 99/20 = 5.95. That's the "expected group size." I get that. Here's where I'm getting confused. Forget math for a minute and suppose you're trying to explain this to your Aunt Petunia. You say: Auntie dear, it's just common sense. Once you've been assigned a group, you have reason to believe it that particular group will be a bigger-than-average group, by the mere fact that you were just added to it. But Aunt Petunia objects: Deary, if you think your group will be bigger just because you were added to it, then every one of those 100 people in the room will be thinking just like you are. Surely everybody in the room cannot validly expect to be in a "bigger than normal" group, can they now, deary? Stumper: With as little math as possible, refute Aunt Petunia. |
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Sep-01-13
| | Sneaky: Upon further reflection I think I clarified my own confusion, although it's still hard to explain it to Aunt Petunia without using math. It reminds me slightly of a "paradox" about friendships: suppose you made a list of all of your friends, then went to your friends and asked them to do the same. Then you took an "average number of friends" that your friends have. You would almost certainly discover than your friends tend to have more friends than you. It's not that you are a loner--almost everybody experiences the same effect. http://en.wikipedia.org/wiki/Friend... Similarly it's likely that your sexual partners are more promiscuous than you, so use protection :) |
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| Sep-01-13 | | kellmano: <sneaky> yeah you're right. you'd explain that everyone could be in a bigger group than the mean average and give the example of 2,0. That said sometimes you just can't explain even basic maths to people sometimes. I remember my sister saying she'd heard a wrong puzzle on the radio, as they asked 'Q. A bat and a ball costs £1.10. The bat is £1 more than the ball. How much is the ball?' According to my sis the answer is definitely 10p. Even when I got coins out to help, she remained unconvinced. |
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| Sep-01-13 | | nok: If there are only two people and you get number 17, you're certainly in a bigger than normal group. Your buddy too. |
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| Sep-01-13 | | Marmot PFL: <Similarly it's likely that your sexual partners are more promiscuous than you, so use protection :)> There was a question here once about men having more sexual partners on average than women, and someone asked whether they wouldn't be the same. Many sources, like Dawkins in Selfish Gene and Diamond in 3rd Chimpanzee, explain why that isn't so, yet a few still insist it is and that the numbers are wrong (which no doubt they are, to a certain extent.) |
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| Sep-01-13 | | Marmot PFL: Actually that gets into differences between mean and median so I shouldn't have said average. |
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| Sep-01-13 | | Marmot PFL: Not that many women will admit to more than 3, although one I knew said "about a hundred" (and she had just turned 21). |
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| Sep-01-13 | | Tiggler: <Stumper: With as little math as possible, refute Aunt Petunia.> If there are 100 people distributed randomly into 20 groups, there will sometimes be a group with no members. I cannot be in that group, so I must be in one of the other 19. The average number in those groups is more than 5. Also, if there is a group with 6 members, and another with 3, I am twice as likely to be in the group with 6. |
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| Sep-01-13 | | nok: <Not that many women will admit to more than 3, although one I knew said "about a hundred" (and she had just turned 21).> From http://en.wikipedia.org/wiki/Scale-...: <The most notable characteristic in a scale-free network is the relative commonness of vertices with a degree that greatly exceeds the average. The highest-degree nodes are often called "hubs"> Your friend was a hub; more often than not though, a less technical term is used. I've met some, too. |
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Sep-02-13
 | | al wazir: One correction to what I wrote: <There are *95* possible outcomes where the group is bigger than 5.95, but only 5 where it is smaller.> <<Tiggler: <<>Stumper: With as little math as possible, refute Aunt Petunia.> [T]here will sometimes be a group with no members. I cannot be in that group, so I must be in one of the other 19. The average number in those groups is more than 5. Also, if there is a group with 6 members, and another with 3, I am twice as likely to be in the group with 6.> Good! I like that better than a derivation using combinatorics. <Sneaky: Similarly it's likely that your sexual partners are more promiscuous than you>. That doesn't sound like an explanation that would be appropriate for your Auntie. |
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| Sep-02-13 | | Tiggler: <al wazir> But here is a cute bit of combinatorics: Probability of a random group having five members when 100 items are distributed randomly among 20 groups = 0.18 . Probability of a random group having six members = 0.15 . Expected number of individuals who are members of a group of 5 = 20*0.18*5 = 18 Expected number of individuals who are members of a group of 6 = 20*0.15*6 = 18 Hence probability of any individual belonging to a group of 6 = probability of belonging to a group of 5 = 0.18 . So no particular individual is special in this regard. |
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| Sep-08-13 | | PinnedPiece: Ok, ok,
OK! Due to overwhelming demand for the answers, I now provide the conclusion of ==== Zoned out on Time ====
1. Which country on the planet will never ever have the same time as any other country? http://www.worldtimezone.com/time/w...
http://www.worldtimezone.com/index2...
Nepal is five hours and 45 minutes ahead of UTC (GMT). Nobody else does that, nor probably ever will. 2. Fastest three days:
d) None of the above
You can accomplish this in a few seconds. Just before Monday midnight, slip west across the International Date Line, to make it Tuesday for a few seconds before it turns Wednesday. http://upload.wikimedia.org/wikiped... 3. Daylight savings
How many "time zones"--or different official clock values--can there be on the earth at any given moment? http://en.wikipedia.org/wiki/List_o... http://www.worldtimezone.com/index2...
Answer: 40 (or more) but the daylight savings time is a red herring. Whether a country goes with it or not, it will still have the "same time" as some other country, and that will not increase the number of official clock zones. --- --- --- --- ---
There. Now get off my back!
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| Sep-08-13 | | Jim Bartle: Thanks, PinnedPiece. Now I can finally get some sleep. |
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Sep-08-13
| | al wazir: <PinnedPiece>: I could have answered some of the questions, but I didn't take your quiz because the answers are based on arbitrary rules. It's hard for me to take such questions seriously. The answers aren't a logical necessity like mathematical truths or facts of nature like one of your previous questions about meteorites. The problem is that time zones themselves are arbitrary. Congress enacts a new starting or ending date for daylight saving time every couple of years, and I recall reading that in some mid-western state (Illinois? Indiana?) or part of that state there is a time zone that's staggered by half an hour from its neighbors. (I don't know if that's still true.) And a few years ago Alaska switched to a single time zone for the whole state, which -- considering that it spans about 45 degrees of longitude -- is absurd. Edgar Allan Poe wrote a story, apparently before the International Date Line was established, on one of your themes. (The suitor of an heiress would be allowed to marry his beloved only when "three Sundays in one week" occurred.) |
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| Sep-08-13 | | Jim Bartle: Do you remember the name of that story? |
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Sep-08-13
| | al wazir: <Jim Bartle: Do you remember the name of that story?> "Three Sundays in a Week." |
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| Sep-08-13 | | PinnedPiece: <aw: I recall reading that in some mid-western state (Illinois? Indiana?) or part of that state there is a time zone that's staggered by half an hour from its neighbors.> That would be a little piece of N.Western Indiana, from the IL border over to Valparaiso, which abides by Chicago time since they are in its area of influence. But they aren't offset by half an hour. The rest of Indiana is Eastern time. I only know this because I have worked extensively with a power company up that way recently. . |
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| Sep-09-13 | | tbentley: It looks like Venezuela is another answer for the first question, since it doesn't use Daylight Savings Time. |
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| Sep-09-13 | | PinnedPiece: < tbentley: It looks like Venezuela is another answer for the first question, since it doesn't use Daylight Savings Time.> Well, if that means Venezuela will be on the same time as any other country (or time zone) as a result, then it is not an answer to #1. . |
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Sep-09-13
| | Sneaky: I learned recently that most of Antarctica has its own time zone, namely GMT. That way, the people at the research stations down there know how to set their watches. I wonder if it works the same way at the north pole? |
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| Sep-09-13 | | Tiggler: Tell me, Pinned Piece, is MST the same as PDT, even though the time is nominally the same? No one I know can schedule a teleconference correctly when one of the participants is in Arizona. They do not know that MST and MDT are different. |
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| Sep-10-13 | | PinnedPiece: <Tiggler> Arizona never adopts Daylight Savings Time so from March/April something* through November something Arizona is on the same time as PDT, or California, Oregon & Washington time in the summer. That means it is one hour later than other Mountain Time states (Colorado, Utah, New Mexico, etc.) <USA, Canada clocks on Daylight Saving Time until Sunday 3 November 2013 at 2am local time> http://wwp.greenwichmeantime.com/ti... From November something through March/April something, Arizona is on the same time as Colorado, New Mexico, etc. That means it is one hour earlier than California. Perhaps the thing to do is note that Arizona is permanently GMT -7. -- --- --- ---- ---
* It seems open to negotiation every year.
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| Sep-10-13 | | Tiggler: <PP> I live in Arizona, so I know about what you posted. My question was about semantics: Even though an observer in orbit sees that my clock now shows the same time as a person's clock in CA, are we on the same time? Maybe not, because I am on MST but the clock in CA is on PDT. When I first moved here, I asked a long-time resident why no daylight saving in AZ? The answer was that we have all the daylight we can cope with here. |
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