Results 1 to 5 of 5

Math Help - Birthday Paradox Problem!!

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    4

    Exclamation Birthday Paradox Problem!!

    Hey guys, anybody got any ideas on how to do this ?

    We all know that the probability of finding two people in a room with the same birthday becomes better that a half when there are more than 23 people in the room. How many have to be in the room before the probability of two pairs of people with the same birthday is better than a half?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Dec 2008
    Posts
    52
    Nice question...

    I have no idea.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    Meh
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by Bruce View Post
    Nice question...

    I have no idea.
    Quote Originally Posted by Rule #17
    Only respond to questions where you have a sufficient knowledge of the topic to give helpful input. It is not helpful to make a hopeful guess or stab in the dark if you have no idea what's going on. This might in fact cause a delay in the question getting a competent response.
    Please read the rules!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by jessismith View Post
    Hey guys, anybody got any ideas on how to do this ?

    We all know that the probability of finding two people in a room with the same birthday becomes better that a half when there are more than 23 people in the room. How many have to be in the room before the probability of two pairs of people with the same birthday is better than a half?

    Thanks
    Make google your friend.

    Eg.

    Birthday problem - Wikipedia, the free encyclopedia

    The Birthday Paradox :: curiousmath :: math is an attitude

    The Birthday Paradox

    HowStuffWorks "Someone told me that if there are 20 people in a room, there's a 50/50 chance that two of them will have the same birthday. How can that be?"

    etc. etc. etc.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by jessismith View Post
    Hey guys, anybody got any ideas on how to do this ?

    We all know that the probability of finding two people in a room with the same birthday becomes better that a half when there are more than 23 people in the room. How many have to be in the room before the probability of two pairs of people with the same birthday is better than a half?

    Thanks
    Suppose there are N people. Let X be the number of pairs of people with the same birthday.

    What "we all know" is how to compute P(X\geq 1), and this is done by writing P(X\geq 1)=1-P(X=0)=1-\frac{365\cdots (365-N+1)}{365^N}.

    What you want now is P(X\geq 2)=1-P(X=0)-P(X=1), so it remains to find P(X=1).

    We have P(X=1)=\frac{\mbox{\# sequences of $N$ birthdays with exactly one matching pair}}{\mbox{\# sequences of $N$ birthdays}}. The denominator is of course 365^N. As for the numerator, it decomposes into the number of ways to choose the matching pair and the number of ways to choose a sequence of N-1 different birthdays. So we get: P(X=1)=\frac{\frac{N(N-1)}{2}365\cdots(365-(N-1)+1)}{365^N}.

    Finally, P(X\geq 2)=1-\frac{365\cdots (365-N+1)}{365^N}-\frac{\frac{N(N-1)}{2}365\cdots(365-(N-1)+1)}{365^N}. It would be possible to simplify the writing a bit. Anyway, you can have the values computed by a software or a calculator for, say N=20,\ldots, 40. And you find (well, at least I find, you should check it) that 36 people are enough to make the probability of double matching greater than a half.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. birthday paradox
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: May 8th 2011, 08:35 PM
  2. Social Security Number/Birthday Paradox problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 16th 2010, 07:21 AM
  3. Birthday Paradox
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 27th 2010, 02:58 PM
  4. Birthday Paradox
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: March 26th 2010, 05:29 PM
  5. Birthday Paradox Math Project
    Posted in the Statistics Forum
    Replies: 8
    Last Post: November 29th 2009, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum