The Facebook Birthday Problem:
This problem stems from the classic Birthday Paradox.
It says:
How many friends do you need for the probability of having at least one friend with a birthday each day to be greater than 50%?
Answer: If there are 23 friends, the probability of two or more people sharing a birthday exceeds 50%. If there are 60 people, the probability exceeds 99%.
If there are birthdays every day among my friends on Facebook, and I want to send birthday wishes to them every day, how many friends do I need to achieve this daily occurrence? How is the probability calculated?
Q1-1: If I have 1000 friends on Facebook, what is the probability that there will be a friend's birthday every day?
Q1-2: If I have 5000 friends on Facebook, what is the probability that there will be a friend's birthday every day?
Q2-1: How many friends do I need at least to ensure that there is a friend's birthday every day with a probability of more than 50%?
Q2-2: How many friends do I need at least to ensure that there is a friend's birthday every day with a probability of more than 99%?
(Calculations are made without considering leap years.)
This problem is not really a "Birthday Problem", but more like a "coupon collector's problem".