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Probability Of Having Same Birthday

Probability Of Having Same Birthday - 6 july

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

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27 comments:

  1. 32, If year and month is not taken into consideration ...

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    1. OMG, its two, if you get identical twins, then there really isn't any way they can't share a birthday. 100% they share a birthday.

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    2. Why not three for triplets? Etc.

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  2. 23, yeah. year and month not taken into consideraion.

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  3. Say one person already in room. Second enters. now probability of him not sharing b'day is (364/365)=x. Now third one enters, probability now of not sharing is (x*363/365=x).
    keep on going like this.
    take the product for n persons. let it be y.
    now (1-y >1/2) solve for y(in terms of n) to get 23.

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    1. This is the correct answer, but I couldn't follow your explanation. Wikipedia has an article on this. Probability is a very strange subject, with non-obvious answers.

      http://en.wikipedia.org/wiki/Birthday_problem

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    2. prob of 2nd person having the same date = 1/365, prob of 3rd person havin same date as either that of 1st or 2nd person is 2/365, similarly prob of 4th person having the same bday as other 3 is 3/365.........now all these added together should be >= 0.5 .....so 1/365+2/365+3/365+........n/365 >= 0.5 ........to find minimum value of n ........1+2+3+4+....n >= 365/2 ........or n* (n+1)/2 >= 365/n........or n*(n+1) >= 365 or n should be minimum 19 considering the 1st person the final answer is 20 ........so with 20 people in a room the probability is greater than 0.5 actually its 0.52.....By Kaustubh

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  4. 184
    Suppose, person X born on 1st Jan.
    Probability of another person to born on the same day would be 1/365. so, probability of n persons to born on same day will be n/365 (As all these events are mutually exclusive events).
    so, n/365>0.5 ... n = 183.
    Total persons = 184 (including first person X)

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  5. 2 cuz just get twins to come in the room...

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  6. Well.. why did we not consider leap year???

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  7. Twins can have diff birth days - 1 11:59 pm, the other oo:01 am

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    1. Yes, twins have a slight chance of being born on consecutive days. However, the chance of the twins being born on the same day is still /more/ than 50%.

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  8. 366, one for each day of the year, + one more to turn it into a 100% chance of there being two people who were born on the same day, (wich is more then 50%!)

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  9. I would like this one better as minus the date. You exclude the math and add the confusion:-)

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  10. Peter Pan - forever youngNovember 6, 2012 at 10:59 PM

    The answer is 3. The question is talking about probability not reality if that makes sense. If there are 2 people in the room then there is a 50/50 chance that that they are the same birthday but if there is 3 people there is a greater than 50/50 chance that 2 have the same birthday.

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  11. if there are 365 ppl inside

    then 365 => 1/365 (for having different birthday)
    if 365 + 365 => 2 / 365
    if 365 * 3 => 3 / 365
    if 365 * 193 => 193 / 365 which is greater than 1/2

    total number of ppl should be 365 * 193 = 70445

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  12. 2. If you put 2 people in a room, they either share a birthday or they don't. 50%

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  13. 3. If there are 2 people in the room, they either have the same birthday or they don't. 50%. So, if there are 3 people in the room, the chances are greater than 50/50

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  14. just put twins in the room haha

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  15. Triplets. So 3. I still think this makes more sense than the actual answer

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  16. 2 they either do or don't have the same birthday 50/50

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  17. prob of 2nd person having the same date = 1/365, prob of 3rd person havin same date as either that of 1st or 2nd person is 2/365, similarly prob of 4th person having the same bday as other 3 is 3/365.........now all these added together should be >= 0.5 .....so 1/365+2/365+3/365+........n/365 >= 0.5 ........to find minimum value of n ........1+2+3+4+....n >= 365/2 ........or n* (n+1)/2 >= 365/n........or n*(n+1) >= 365 or n should be minimum 19 considering the 1st person the final answer is 20 ........so with 20 people in a room the probability is greater than 0.5 actually its 0.52 .....By Kaustubh

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  18. Four because they said birthday not birth date. So you only have to count Sunday through Saturday

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