A birthday puzzle - Page 2

SheetWise · #11 07-25-2005, 01:38 PM

I wrote a simple simulation and ran 1MM a couple of times --20 came out as the highest frequency both times.

kiddj · #12 07-25-2005, 01:54 PM

I come up with 23rd. (It may be 22nd. I worked it with the chances that the people ahead have not paired up.) My line/logic may be flawed though.

LetYouDown · #13 07-25-2005, 01:57 PM

I'm still trying to figure out what I messed up. I just ran through an array with random numbers between 1-365 to represent the days (ignoring leap years). As I randomized each date, I compared it to all previous people in line. If it matched, saved it and continued to the next trial. Then I divided by the number of trials.

Edit: Is it more accurate to look for the most common occurring element or the mean for this problem?

durron597 · #14 07-25-2005, 03:00 PM

You should stand 23rd in line. The reason being is that the more people in front of you, the more likely it is to have already occurred. Since 23 people is the number required for there to be at least 50% chance of two people having the same birthday, you expect that any spot after that in line it has already occurred.

PairTheBoard · #15 07-25-2005, 03:08 PM

Seems like it depends on how long the line is. If there's a billion people in line then someone will almost surely win after the first ticket is purchased. Your best chance of getting in on it would then seem to be by standing second in line.

PairTheBoard

LetYouDown · #16 07-25-2005, 03:09 PM

Huh?

PairTheBoard · #17 07-25-2005, 03:15 PM

[ QUOTE ]
Huh?

[/ QUOTE ]

Huh?

PairTheBoard

LetYouDown · #18 07-25-2005, 03:17 PM

Why would the number of people in line affect the likelihood of the 2nd person's birthday matching the first person's?

Karatitis · #19 07-25-2005, 03:23 PM

Because you would only have 1 birthdate in the pool to match against.

PairTheBoard · #20 07-25-2005, 03:27 PM

[ QUOTE ]
Why would the number of people in line affect the likelihood of the 2nd person's birthday matching the first person's?

[/ QUOTE ]

It wouldn't. But it would effect the chance of any person in line getting more than one shot at it. The game will be over as soon as the first ticket is bought. If you don't match birthdays with the first in line you are just out of luck because you won't get any more chances. But if you do match birthdays your most advantageous place to be is second in line so that someone in front of you who also matches won't take the prize away from you.

PairTheBoard