If there is a group of n people in a room, what is the probability that two or more of them have the same birthday?

If there is a group of n people in a room, what is the probability that two or more of them have the same birthday? It is possible to determine this question by simulation. Write a function that calculates the probability that two or more of n people will have the same birthday, when n is a calling argument.

[mahesh raut]

Let X be the birthdate

Equiation can be given by

Probability=N/(N-X)

[Torsten]

So the probability would be greater than 1 ?

[Image Analyst]

If X is a date, then is N also a date? So what sense does it make to divide two dates?

Answer 1

[Image Analyst]

As this is most likely a homework problem (and I've tagged it as such), I'll just give you some hints.

n = 30;
birthdays = randi(365, n, 1)  % Get list of birthdays out of possible 365 days per year.
counts = histc(birthdays, 1:365) % Count how many people have each birthday.

Put the above in a loop and do it, say, a million times to find the probability that max(counts) >= 2. Try different n also.

Answer 2

[Roger Stafford]

The probability, P, (in a non-leap year) is:

P = 1 - prod((365:-1:365-n+1)./repmat(365,1,n));