So, I have read the birthday paradox problem, and now I came across below question:
Assuming the following: there are no leap years, all years have $n = 365$ days and that people’s birthdays are uniformly distributed across the $n$ days of the year.
(i) How many people must be there in a room before the probability that someone else has the same birthday as you do is at least $0.5$?
(ii) How many people must there be before the probability that at least two people have a birthday on 11th November is greater than $0.5$?
I think the answer to both of the parts must be $23$ people, as we are interested generally in only finding at least $2$ sets of people from $m$ people who have same birthday and then giving this probability.
Any corrections/suggestions/improvements on this is really welcomed. Please let me know whether I am correct?
Edit : Well, for both parts, let's say I have birthday on 11th Nov. Now if I want all people to have distinct birthdays other than that of mine so they can choose days from 364.
So, required probability model is :
$1-\frac{^{364}P_n}{365^n}$
For $n=23$, this works out to be 0.53 and Yes it seems to me I am done.