The standard birthday question is, how many people have to be in a math class for the probability of two having a shared birthday is > 1/2. With standard assumptions about birthday distributions and independence of birthdays.
A slightly different question.
How many people need to be in a stadium for the probability to be at least 1/2 that for each day of the year, two people in the audience share that day as their birthday. Two part question: (a) exclude 29 February. (b) include 29 February.
Can you estimate N in terms of p? I.e. question as posed has p = 1/2. What if we want p >= 3/4?