I've often heard that when you have 25 people in a room, there will be 2 people with the same birthday.?

Question

How is this possible?

I've actually asked some people in my classes in school and at least 3 classes this proved true (and there are about 20-25 people in each of my class) How is it possible?

Answer 1

The birthday problem asks how many people you need to have at a party so that there is a better-than-even chance that two of them will share the same birthday. Most people think the answer is 183, the smallest whole number larger than 365/2. In fact, you need just 23. The answer 183 is the correct answer to a very different question: How many people do you need to have at a party so that there is a better-than-even chance that one of them will share YOUR birthday? If there is no restriction on which two people will share a birthday, it makes an enormous difference. With 23 people in a room, there are 253 different ways of pairing two people together, and that gives a lot of possibilities of finding a pair with the same birthday.

Here is the precise calculation. To figure out the exact probability of finding two people with the same birthday in a given group, it turns out to be easier to ask the opposite question: what is the probability that NO two will share a birthday, i.e., that they will all have different birthdays? With just two people, the probability that they have different birthdays is 364/365, or about .997. If a third person joins them, the probability that this new person has a different birthday from those two (i.e., the probability that all three will have different birthdays) is (364/365) x (363/365), about .992. With a fourth person, the probability that all four have different birthdays is (364/365) x (363/365) x (362/365), which comes out at around .983. And so on. The answers to these multiplications get steadily smaller. When a twenty-third person enters the room, the final fraction that you multiply by is 343/365, and the answer you get drops below .5 for the first time, being approximately .493. This is the probability that all 23 people have a different birthday. So, the probability that at least two people share a birthday is 1 - .493 = .507, just greater than 1/2.

Answer 2

There'd be about a 50% chance that two people in a room of 25 would have the same birthday. The link below goes into some detail about the math and explains it much better than I could.

Answer 3

Although there are 365 days in a year, the distribution of birthdays throughout the year is not even. More people are born nine months after holidays (Christmas, New Years, Valentine's Day). For example, my birthday is about nine months after the 4th of July.

Since the distribution isn't even, the odds become greater that if you are near 25 people, two of them will have the same birthday.

I work at a company with only 17 people and I have the same birthday as a coworker.

Answer 4

Believe this is a trick question that's not a direct mathematical probablity problem. If my assumption is right the tricky word is "birth-day", it's not birth-month or birth-year that counts here. Example: 2 people that have 01/01/1990 and 01/02/1991 birth-dates would consider having the same birth-day because it happen at the first of each month. But that still do not explained how one could guarantee a 100% that 2 person would have the same birthday because the odds only work out to 25/30x2 (considering a month only have 30 days). We need a whole number here not a fraction. ( Thinking......)
My closest guess here would be; the birth-day here actually meant birth-Monday birth-Tuesday, birth-Wednesday so on.... and that would deduce to the real meaning of birth-day to the question. Let's say if I were to ask who in this room of 25 was born on Monday? Odds are there would be 2 or more people raising their hands because everyone was either born from Monday to Sunday. So to guarantee 2 would raise their hands we actually need a minimum of 14 not necessary to be 25 people in a room for a 100%chance that 2 would be born on the same Birth- (Monday,Tuesday,Wednesday.....).

I think I'm wrong here, there're chances that there're more than 2 Birth-Mondays, Tuesday people ... and leaving a single birth-Sunday....person here!
Tell me the answer please!!

Answer 5

In general population, there's a slightly better than 50% chance. In school classrooms (especially elementary), it's very likely because of twins.

If you would like to experiment with this, go to www.random.org and run 25 numbers 1-365 over and over and see how often it happens. I ran it 15 times and it duplicated on 8 of them.

Answer 6

This def finitely happens at the maternity... Imagine a room filled with children, all of them born on the same day.
Now, seriously, how many classmates do you have? How many of them were born on the same day? We were more than 30 boys and girls in my class, but we all had different birth dates. Think about it.

Answer 7

It's called the birthday paradox.

Answer 8

its probability thing. if you flip a coin 100 times it land on heads and tails equal amounts of times, its just a probability

Answer 9

well there are only 365 days in a year, how many people on earth ? what are the odds ?

Answer 10

I am not sure, but i can tell you for sure that if you have 366 people in the room, 2 of them will have the same birthday!