Results 1 to 3 of 3

Math Help - Birthday Probability

  1. #1
    Junior Member
    Joined
    Dec 2009
    Posts
    34

    Birthday Probability

    Hi guys, I have a question that I was talking about with someone a little while ago. The question is as follows:

    If you have 4 people, what is the chances that 2 of them share the same birthday as well as the other 2 sharing a different birthday.

    Example:

    1st Jan, 1st Jan, 3rd May, 3rd May
    or 2nd of March, 20th of December, 2nd of March, 20th December

    All people being on the same born on the same day does not count.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor ebaines's Avatar
    Joined
    Jun 2008
    From
    Illinois
    Posts
    1,037
    Thanks
    282

    Re: Birthday Probability

    The probability that A and B share the same birthday is 1/365. The probability that C and D share the same birthday, but on a different date, is (364/365)(1/365). So the probability that A & B share one date and C & D share another is (1/365)(364/365)(1/365). That's one possible combination of shared birthdays, but there are 2 others: A can share with C and B with D, or A can share with D and B with C. Therefore we multiply the above expression by 3 to get:

     P = 3 (\frac 1 {365})( \frac {364}{365})( \frac 1 {365} ) = 0.0000225, or one in 44,530.33.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2009
    Posts
    34

    Re: Birthday Probability

    Wow that is a very low chance. That makes sense and thanks for the answer!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Probability question, The birthday problem
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 21st 2010, 12:01 AM
  2. Probability of having the same birthday
    Posted in the Statistics Forum
    Replies: 12
    Last Post: February 18th 2010, 03:14 PM
  3. Birthday probability
    Posted in the Statistics Forum
    Replies: 1
    Last Post: November 12th 2009, 09:47 PM
  4. BIrthday probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: January 19th 2009, 08:15 AM
  5. Probability birthday same day
    Posted in the Statistics Forum
    Replies: 7
    Last Post: February 17th 2008, 10:52 PM

Search Tags


/mathhelpforum @mathhelpforum