At least two people have the same birthday If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday?
I tried solving it by taking into account the fact that it will be extremely difficult to solve for the probability of at least having the same birthday and started off by solving it in the complement fashion, where P(at least two people having the same birthday) = 1 - P(every person's birthday is unique), but have been trying to the possible numerator/denominator for this problem. 
 A: Hint:  your approach is a good one.  What is the chance if there are only two people?  Three?
A: You can read all about this famous problem here to learn how to calculate the probability that at least two of $n$ people share a birthday.  In your case at least two of $85$ people will share a birthday with a probability of approximately $99.998\%$.
A: Here is a simulation written in python. It may help you to analyse the problem and understand it.
    import random 
    
    def birthdayMatched(members):
        numYearDa
        ys = 365 # Number of days
        s = range(numYearDays)
        matched = False
        membersList=[None] * members
    
        for i in range(members):
            membersList[i] = random.choice(s)
        if len(set(membersList)) < members :
            matched = True
            
        return matched 
    
    
    def sim_birthdayMatched(numTrials):
        numMatches = 0
        numPeopleInParty = 23
        for i in range(numTrials):
            if birthdayMatched(numPeopleInParty):
                numMatches += 1
        return numMatches/numTrials

Call: The function takes the number of people as an input
sim_birthdayMatched(10000)

Output:
0.5077

