Who is right?

Question

My math professor asked me a question: what are the chances that two people in one room have the same birthday? Thou I knew that it depends on how many people there are in the room and that you can actually calculate the %...but I said 50/50. I could swear that I heard that on some science TV show...thou it does not make cense. Or does it?

Answer 1

"The actual birthday problem is asking if any of the people in the room have a matching birthday with any of the others--not one in particular."

"To compute the approximate probablility that in a room of N people, at least two have the same birthday, we disregard variations in the distribution, such as leap years, twins, seasonal or weekday variations, and assume that the 365 possible birthdays are equally likely. Real-life birthday distributions are not uniform since not all dates are equally likely."

Answer 2

For a class of about 30, it's about a 50/50 chance that SOME pair of people in the room will share a birthday.

Answer 3

This is a pretty well known problem. I am surprised at all the bad answers here. Let's ignore leap years.

The problem is calculated by looking at the probability that N people have different birthdays.

Start with one person. He has a birthday.

The second person has 364 possible dates to avoid having the same birthday. The probability of this is 364/365. So, the probability that they have the same birthday is 1-364/365/

Add a third person. There are 363 possible days he can have a birthday such that the three have different birthdays. The probability of this is 364*363/365^2

There are 362 ways that a fourth person can avoid duplicating a birthday. In general, the probability that they all have a different birthday is

364*362*361*. . . *(365-N+1)/365^

It becomes a 50/50 bet when there are 22 people in the room.


N ........... Probability at least two have same birthday.
2........... 0.3%
3........... 1.1%
4........... 2.2%
5........... 3.5%
6........... 5.1%
7........... 6.9%
8........... 9.0%
9........... 11.2%
10.......... 13.6%
11.......... 16.2%
12.......... 19.0%
13.......... 21.9%
14.......... 24.9%
15.......... 28.0%
16.......... 31.1%
17.......... 34.3%
18.......... 37.6%
19.......... 40.8%
20.......... 44.1%
21.......... 47.3%
22.......... 50.5%
23.......... 53.6%
24.......... 56.6%
25.......... 59.6%
26.......... 62.5%
27.......... 65.3%
28.......... 67.9%
29.......... 70.5%
30.......... 72.9%
31.......... 75.2%
32.......... 77.4%
33.......... 79.4%
34.......... 81.3%
35.......... 83.1%
36.......... 84.8%
37.......... 86.3%
38.......... 87.8%
39.......... 89.1%
40.......... 90.3%

Answer 4

What is there are only 2 people in the room? Would the odds be that same if there were 1000 people in the room?? Ofcourse not. It all depends on how many people are in the room.

Answer 5

50/50 is ridiculous, unless there are 182 1/2 people in the room.

Answer 6

It depends on the number of people

Here it is: (Number of people / 365) * 100%

So if there's two people, then it would be .548%

If there were 182 it would be close to 50%

Answer 7

yes