All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Birthday Line (Posted on 2004-03-29) Difficulty: 3 of 5
At a movie theater, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone 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, that birthdays are distributed randomly throughout the year, etc., what position in line gives you the greatest chance of being the first duplicate birthday?


See The Solution Submitted by Victor Zapana    
Rating: 3.5556 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): Function [with observations] | Comment 14 of 21 |
(In reply to re(2): Function [with observations] by Richard)

What I did was simpilify the problem.

I supposed there was a 6 day 'year' and stated making a tree diagram.

P(1) = 0/6 (Six days, none are winners)
P(2) = 6/36 (36 pairs of days, six are winners)
p(3) = 60/216 (216 trios of days, 6 ways to match 1st person times 5 ways to match second times 2 winning days)
p(4) = 3x4x5x6/6^4
p(5) = 4x3x4x5x6/6^5
p(6) = 5x2x3x4x5x6/6^6
p(7) = 6x1x2x3x4x5x6/7^6

I figured this was right because these added up to 1

For 6 days in a year maximum probability p(3)=p(4)
Once I had a formula I made a TI-83 calculator program to make a list of probabilitites for each number of days to see what the max. prob. was for each.

The numbers with ties were 2, 6, 12, 20, 30, 42, 56, overflow (57^58 is too big)
with ties for 2&3, 3&4, 4&5, 5&6, 6&7, 7&8, 8&9 respectively.
This fits a polonomial of degree two. I can't see how to prove it does, so it will have to do.

Hope this makes a shred of sense.


  Posted by Jer on 2004-04-02 14:32:18

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information