last post about the AP reading (i promise):
my day: get packet of 25 essays. essay 1: open blue book (it's actually pink), find question #4, read, record score, close. essay 2: same thing. YES, I'VE DONE THIS 1,925 TIMES.
on each packet is the student's ID number, initials, and date of birth. for the past two days i've entertained myself with this game: how long will it take me to find a student with the same birthday as me?
day 1: it took 185 essays before i found one with the same birthday as me. this student scored a 0/5 on my question. i was very disappointed in my birthday sharer.
day 2: it took 125 essays before i found one with the same birthday as me. this kid scored a 4/5! good work, birthday sharer! and then like 10 essays later i found another kid with the same birthday as me. less exciting this time...i don't remember what the kid got.
now, the question is: how many essays SHOULD it take to find one with the same birthday as me? [dad or rachel-in-waco: figure out the math for me. i am too tired to do so myself...] i don't know the answer, but this essay is interesting in that it addresses (sort of) the same principle, mathematically. (thanks to dad for reminding me of this!)
182.5, right?
ReplyDeleteIf there is a 1/365 chance of any given paper having your bday (actually, 4/1461 if we count Feb 29), after 182.5 papers, the cumulative probability of seeing that date will be 50%. So, if the sample size is large enough (i.e. you grade a lot more than 2,000 papers), and you average the number of papers you have to read before you find your bday, it will fall close to 182.5.
- Rachel
I dont know the answer to your question but I pose another interesting fact. In a group of 23 people there is more than a 50% chance of 2 of those people having the same birthday (day...not year...and minus 2/29)!
ReplyDeletehttp://en.wikipedia.org/wiki/Birthday_problem
awesome, rachel - thanks! so my 185 was actually pretty right on, and the 125 day was a lucky one. or statistically normal? i mean, i guess the odds are the same for me to find my birthday on the first paper or not until the last...if we were betting, though, we'd say it was by the 182.5th paper? i think?
ReplyDeletethomas, get with the program - i linked to that in the post! though i do appreciate that you know about the same birthday phenomenon thing that i do. :)