Questions tagged [birthday]
Birthday problems typically look at probabilities and expectations of a random group of individuals sharing birthdays and how this changes as the number of people increase. They often assume that individuals' birthdays are independently uniformly distributed across 365 days but similar problems can use other numbers or assumptions. They can be generalised to wider occupancy and collision problems.
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Birthday problem: Poisson vs binomial random variable
From this post, the birthday problem involving more than 2 people can be approximated using a Poisson random variable. But I am wondering whether a binomial random variable can be used here. I imagine ...
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Birthday Paradox at least Vs Exactly
The famous paradox in probability theory, the Birthday Problem asks that:” What is the probability that, in a set of n randomly chosen people, AT LEAST two will share a birthday.”
In some other books ...
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Birthday paradox - variance, parallelisation, simple proofs?
I am looking for an elementary proof of the fact that expected time for finding a colision with $n$ bins is $\sqrt{\frac{\pi n}{2}} + O(1)$. The proof that I knows relies on the asymptotic expansion ...
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What is the probability of sharing a birthday if a year has an infinite number of days?
Here is the problem:
Suppose that there are $k$ people. Each of them independently picks a uniformly random number from the set $\{1, 2,...,n\}$. We say that a collision happens if there exist two ...
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How many days with birthdays are in a classroom?
Assumption:
I am a teacher of a classroom with n students. And every time there is one or more birthdays in a day, I will buy only a cake.
Question:
How many cakes do I have to buy on average every ...
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Probability - Birthday paradox
Let us assume every child in the world has a random and uniform favorite number between $1$ and $m$, and also has a different random and uniform unfavorite number between $1$ and $m$.
Denote $E_{k,m}$ ...
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Birthday problem with really high parameters
I have $n$ objects. Every object has a random value in $[0;k)$ (in $\mathbf{N}$).
How high is the probability for every object to be unique within the set of $n$ objects?
This is obviously a case of ...
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Approximating an inequality with extremely large numbers
I am trying to work out the number of 12 item sequences needed to have a greater than 50% probability that two of these are the same. So far, I have got
$$
1 - \frac{2048^{12}!}{\left(2048^{12}-n\...
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Derivation of Birthday Paradox formula with unknown n
I have been trying to derive the formula for the upper bound probability of the birthday paradox for any number of occurrences $n$.
Assuming we want to find the number of occurrences $k$ such that ...
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Probability of Adjacent Birthdays
Recall the birthday problem, where only 23 people are required for a >50% chance that at least two share the same birthday.
What is the new probability if we want at least two people out of twenty-...
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Why numerator of the second term (365!) greater than the denominator (355!) for the probability that none of the 10 individuals share a birthday?
10 random people gather in a room. A researcher is inquiring if any two share a birthday (month and day). None of the individuals were born in a leap year.
The probability that none of the 10 ...
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Birthday problem with indistinguishable clones.
Suppose we have created an army of n clones which are completely identical(except they may have different birthdays). The cloning happened at different times such that all 365(disregarding the 366th ...
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What's the probability of 5 people not sharing the same birthday including leap years [duplicate]
What's the probability of 5 people not sharing the same birthday including leap years
Would it be: $$\frac{365(364)(363)(362)(361)}{(365^4)(366)} = 97.02\%$$ because every $4$ years is a leap year ...
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What are the odds of 3 out of 8 people sharing the same birthday? [closed]
I work on a team of 8 people. Three share the same birthday. I'm no mathematician but I imagine the odds are literally astronomical in measure.
A figure in this instance may be meaningless to me. Does ...
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Probability that there exist at least one day without any Birthday
Probability that a given day do not have any birthday among N people is: (364/365)^N
However, what will be the probability that there exist at least one day in a year that have no birthday?
This ...
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