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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?

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

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.

2. Why not three for triplets? Etc.

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

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.

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

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

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)

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

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

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

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%.

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%!)

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

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.

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

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

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

14. just put twins in the room haha

15. at the babies' room at the hospital.

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

17. 2 they either do or don't have the same birthday 50/50

18. 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

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