Tuesday, May 11, 2010
Problem 1: The Birthday Line
At a movie theater, the manager announces that a free ticket will be given to the first person in line whose birthday is the same as someone in line who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year, what position in line gives you the best chance of being the first duplicate birthday?
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i think either 365/366 or 12 in line. I think his because after a year, or a year's amount of people would lead back to day 1, your birthday. also 12th because there are twelve months in a year, so its possible that the first person in line has the same month (and day) as you!
ReplyDeletei believe i missread the question... you should be in line 1st! it says that you have to have the same birthday as someone who bought the ticket, it never says they have to buy the ticket first... you would probably win the contest because once you purchase your ticket first, you just have to wait for someone with the same birtgday. this is a lot easier than hoping that someone before you has had the same birthday as you...
ReplyDeleteIris
Iris,
ReplyDeleteIf you're first, then no one else has said they have the same birthday! I think it's if someone has it BEFORE you, not after you. I'm still thinking of the answer...
Katty
I think being 366th in line would give you the best chance of winning. This is because you have to assume the first 365 people all have different birthdays, meaning the 366th person is the first person to have a chance at repeating a birthday. If through the first 365 people, every birthday has occurred then the 366th person is guaranteed to win.
ReplyDeleteMs. Dimitry did you mean informally
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ReplyDeleteYou would have the best chance if you were 366th because the first 365 people would take up most of the birthday's of the year. If you went 366th, then you would be most likely to have the birthday someone else had.
ReplyDelete(as the people said before me) u have the best odds at going in 366th spot because u have 365 assorted birthdays ahead of u
ReplyDeleteWell, I know this might sound weird, but I think December 7th is a pretty common birthday. There used to be someone in my class also born Dec. 7. There are more common birthdays (like October 18th or December 31st) so I would go right about 190-210. There is a pretty high chance someone out of 200 people have the same birthday as me.
ReplyDeleteIn my opinion the whole thing is a game of chance. THEORETICALLY, if you get in line 366th, then you should have the first duplicate birthday. However, if you get in line second, you still have a chance that the 1st person in line has the same birthday as you. It also says you have to be the FIRST person with a duplicate birthday, so really, even if you get in line 366th, a person could already had a duplicate birthday. So really the way I see it is that it's a game of chance. You have a 1% chance that someone before you will have a birthday the same day as you. Theoretically, if you came 366th in line you would have a much great chance of becoming the first duplicate then someone say, in line second. Also being in line 1st doesn't make sense either theoretically or experimentally because there's no one in front of you to have the same birthday as you! As for what Davin said about the common birthdays, I think that you can take from your own expierence common birthdays, but in reality you would have to take a tally of say, 100 people to find out really what are the most common birthdays. I do agree if you knew the most common birthdays for sure Davin's theory would make sense, but otherwise I don't think it would work. In conclusion, I believe that theoretically you have the greatest chance being in line, but in reality, it's just a game of chance.
ReplyDelete*KATTY*
p.s. I really like the math blogs this week thanks Ms. Dimitry!
wow that was long
ReplyDeleteThe question says that the birthdays are distributed uniformly throughout the year. The question is silent as to the order of birthdays in the line. I will assume birthdays are randomly distributed in the line. The question does not state how many people line up. Assuming that there are 366 people in the line you can win no matter what if you are last because there is no one else except you with a birthday that it the same as someone else’s. If you have more people than 366 for example 730, it is completely random and it is impossible to make a right choice. It is like the lottery. If there are less than 366 people for example 100, it is just as random as when there are more than 366 people in the line.
ReplyDeletei think it depends on how many pplz are in line but im probably wrong about that soo... you should probably be 366th in line (or the first day of next year) 'cause theres a huge range of birthdays yearly, so if u came last after all of that, there would be a quite high chance of you getting the free ticket. i think XP
ReplyDeleteWell I think that you would have to be 366th in line to win. My reasons for this you ask? Aaah well here they are: In a year there are 365 days, there is a birthday everyday. If you are 336th in line there are 365 people in front of you, it is likely that all the people in front of you have a different birthday over the course of 365 days because there are 365 people. if they all do have different birhtdays and you are 366th you are the first person to not have a birthday over the course of that 365 days so you must have a birthday shared with someone else. i hope that isn't too confusing! :):):)-emily
ReplyDeletethis is to davin
ReplyDeleteu realize that ur class is a very small portion of the world. Also more babies are born in summer rather than the winter because it is a warmer time and easier to celebrate in the summer.
chris thats not why! (babies r born in summer)
ReplyDeleteI agree with katty's previous post, that it is a game of chance. It might be safe to go 366, but really, going 366th does not guarantee you a free ticket, it just makes more sense to go that spot in line because obviously, the first 365 people in line will have varying birthdays and will not have the same birthday. However, you need to consider the fact that only the first person who has the same birthday as someone else wins tickets, so going 366th gives you almost no chance to win tickets, because there is bound to be at least 2 people out of 365 that have the same birthday. If the manager was giving out let's say, tickets to the first 20 people (or more) that have the same birthday, chances that you will get a ticket will be higher if you go 366th in line. But that is not the case, so really, you either go 366 and you will probably miss your chance to win tickets, but at least you will have some chance, or you could go comletely randomly, but a bit later in line, like in the 50's to 100's, and have a very slim chance but you will still have a chance. So, theoretically, you should go 366th. In reality, however, it doesn't really matter because you have no idea who gets in line and what their birthday's are, so it is all chance.
ReplyDeleteAlso, to add on to the debate of when the most babies are born: I searched it up, and in the U.S. the most babies were born in July, August, September. This is because some women, like teachers, have the summer off, and they do not want to leave school during the school year because they are pregnant. So they plan ahead and make sure that their baby is born in the summer.
If you went after 365 people then your chance of getting first duplicate is the strongest because at least one would probably have the same birthday as you...................i think.....................
ReplyDelete$$$EM$$$
i think you have a high chance of wining would either be 365 day or 366th day in otherwars the first day. my reason is because for one thing, both 365, and 366 have a high chance of wining, but 366 has a higher chance because it has 365 people before you which is a equivilent to a year in days.this is because at least 300 of the 365 birthdays have to be infront of you if you are the 366th person, that raises the chance, also if 300/365 people before you have different birthday's, theoretically you should win because you are 1/365 birthdays and that leaves 64/365 birthdays not there, but 64/365 compared to 301/365 clearly 301/365 has a higher chance.
ReplyDeleteAdele
This is an impossible question with no right answer!!!!!! if i wasn't the pesron waiting there i qould choose the number 133,225 simply because that is a big number and there is a very high chance you'll get a ticket.(Also because 133225 is 365 x 365) If i was the one waiting for the ticket i would choose the number i saw many times while scrolling down the page..............it was 366, oh yeah there was also 365, which is a little shorter but has 1 less chance of getting a free ticket. La La La La and also like how everyone else explained it, there are 365 days in the year we are talking about,(as it says in the text) and each day has a possibility of having a birthday, so by being number ....um......366 you have a chance of getting it and also because that is the number after the whole year!
ReplyDeleteThere is no completely right answer to the question because if its any number before 366 its not a guarenteed win because if it is a number after 365 it is not the highest chance because there might be a chance that somebody in the 365 range may have already won so there is no right answer it is just luck.
ReplyDeleteThis is a pretty vague question, or hard to intepret. You would think that if you were the 366th person in line, you would be first to get a double birthday, theoretically. Here's how it works: If they are 365 birthdays in the year, and 365 days in a year, then if you were 366th you would have the first double birthday, because it starts the next year. But here's the trick, birthdays are distrubited randomly through out the year, so someone could already have a double birthday, and that's what you don't know. But anyways I still think that you should be 366 person in line.
ReplyDeleteum, 366th plus becuz then if everyone hass diff bdays, assuming they do, than urs has 2 match one of em, so thats basically it, after 366th theres a risk someone will win b4 u, becuz they have all been chosen so if u can get there fast enugh 366th
ReplyDeleteWell i think that the 366 would be the best because it says "Assuming that you don't know anyone else's birthday, and that birthdays are uniformly distributed throughout a 365 day year?"
ReplyDeleteThat would mean that 366 would be the best because you would have to win
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