My question is: Find the probability that at least 2 people in a room of 30 share the same birthday.
the way to solve this problem is 1 - P(unique birthdays) which is quite straightforward.
But, Q1: how to solve it the other way around? Instead of finding unique birthdays, just find P(Same birthdays). How would that happen?
I thought if everyone from 2 to 30 ppl share 365 bdays and order matters then,
365Pr / 365 where r = 2 to 30
and then summing them up will give the total probability
sum([permutation(365,ppl)/365 for ppl in xrange(2,31)]) Decimal('5.965783049451056333110639647E+73')
Evidently that's not the case. so how to solve #1 ?
Q2: What if there were 1000 people in a room since 365 < 1000, how would that go?
With the Q1, what I mean is the chances 2 people share the same bday and 3 ppl might share some other day, while 4 ppl might not share the same day, 17 ppl might share some other day. For the sake of academic discussion, however complex this might be, I am only interested in knowing how does one solve this, say if we reduce the number of people to 5 just to reduce the complexity, I still would like to know how to approach this problem.
UPDATE ON Q1 Specifically I am asking what is the method/logic to calculate problems on such conditional probability?
Say, there are 4 genes discovered so far and 6 bases in total; What are the Chances of 2 or more genes sharing same bases.
Given 4 genes ('ABCD') there are following sets of possibilities: [['AB', 'CD'], ['AC', 'BD'], ['AD', 'BC'], ['BC', 'AD'], ['BD', 'AC'], ['CD', 'AB'], ['ABC'], ['ABD'], ['ACD'], ['BCD'], ['ABCD']]
So what are the chances?