How many people do need to have in one room for two of the people to have their birthday on the same day?

Question

During a discussion at work someone said it was 23! so I'm curious?

Answer 1

The chance of having two people with the same birthday is over 50% when 23 people are in the room.

It doesn't reach 100% until there are 366 though (or 367 if we count Feb. 29th births).

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For the mathematics behind this...

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(When not counting leap year days and considering all days of birth to be equally probable...)

The simplified probability of nobody having the same birthday is given by:

365! / [ 365ⁿ (365 - n)! ]

where n is the number of people in the room.

In case you are wondering, ! is the factorial function.

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

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When there are 23 people, this becomes:

365! / [ 365²³ (365 - 23)! ]

≈ 0.4927

Thus, the probability of two people having the same birthday is approximated by:

1 - 0.4927

= .5073

So there's about a 50.73% chance for two people to have the same birthday if there are 23 people in the room.

Answer 2

I think earlier answer by gravitative is the right one .... but being fairly baffled by the maths I have carried out a very unscientific experiment.

Take starting 11s of 1st premiership game of season Arsenal v West Brom plus ref gives you 23 people. Do any of them share a birthday?

Rather spookily there are THREE matches:

Howard Webb / Do-heon Kim - 14 July

Carl Hoefkens / Abdoulaye Meite - 6 October

Paul Robinson / Chris Brunt - 14 December

My brain hurts ....

Answer 3

I'm sure i've read that it's 23.

Answer 4

You need to have at least 366 people to make sure that two of them have the same birthdays. Assuming each person has his or her birthday on each day of the year, the 366th person will surely have his birthday in one of the other 365 persons.

Of course you can consider the leap year which adds the 29th of the february in the calendar. In this case, you need at least 367 people in the room.

Answer 5

31! Im just guessin cos there is 31 days in a month (most months) so more likely :)

Answer 6

To be certain you would need 367. This is because there are 366 days in a leap year, if you have one person for each day of the year then one more person would make it certain that there would be a couple of people with the same birthdays.

With 23 people or more I think it becomes about 50:50 that you have 2 people with the same birthdays. If you have more than 70 people in the room it becomes really probable that 2 people have the same birthday.

I worked it out by taking the probability that none of the people have the same birthday as one person (22 people in the rest of the group and 365 days remaining in the year). Then I assume that this is true and find the probabilty that the next person shares his birthday with none of the rest (1 fewer person in the group and 1 fewer day in the year). I continue this until there are no more people left then I multiply all the probabilities together.

Answer 7

well you could have two people in the same room both having the same birthday so it's down to chance. To be sure of having two people with the same birthday you'd need 366 people

Answer 8

2 my sister and me.

Answer 9

It depends on what your asking.  Define the same day?  It would be 366 if your talking about everyday in a year.  Or it could be eight because there are only 7 days in a week.

Answer 10

Easy ,its 2. Think about it. Its a trick question, there not asking for the odd's, just how many people it would take......... which is Two!

Answer 11

well my wife was born on her mums birthday so they have the same birthday date

Answer 12

Well, if all things were equal you would expect that if you had 365 people in a room then each day of the year would be covered by a person having a birthday. Adding another person would mean one day is duplicated.

This isn't quite right because some days have more people born on than others (for example 9 months after christmas is a more common birthday than say, 9 months after 18th January) and that means that you need fewer people than 365 - the more common birthdays will get duplicated. What the number is I am not sure, but I am fairly sure it is more than 23 people.