In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.

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### A variation on the birthday paradox

A question to the community: Given N persons, and a period of M months, what is the probability at least one will have a birthday within the period? P(bday in period) = N * (1/12) * (M/12) This 'feels'...
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### How to determine the likelihood a random number generator is using a uniform distribution?

Let's say I have a blackbox function generate_number() that generates a random number between 1-N; and assume N is known. Each ...
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### Birthday puzzle

I need some help with Bayesian statistics likelihoods. Consider the following question: Given a number of persons. Each person $p$ knows $n(p)$ other persons – $p$'s neighbourhood $N(p)$. Knowing a ...
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### How do you find quantiles in this balls-in-bins problem?

I need to calculate the expected number of hash collisions with a range for a software project. I think this is a reformulation of the birthday problem, as follows. Suppose you have $n$ balls ...
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### Drawing a random sample without replacement from data set

I have data generated by a RCT with a control and treatment group, each with n=300, so N=600. The observations are assumed to be i.i.d.. From that population, I'd like to draw 5 random observations ...
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### Maximum Likelihood Estimator on birthday paradox

I am looking into some properties of some hash functions. It is rather a short hash $16bit$ which yields up to $65536$ different values. Given that I have $M$ samples which populate $N$ out of $65536$...
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### Generalized birthday problem plus spouse

Suppose a group of persons, say of size N (who are all married), are in a room. For any given N, I would like to know the probability of at least two people in the room sharing the same birth date (...
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### How to calculate this dependent probability (marbles without replacement)?

I present the question in two steps: First: Let there be 100 bags. A person puts 5 marbles into 5 separate, randomly selected, bags. You are now to collect the contents of the bags, one by one. If you ...
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### What is the probability of 4 person in group of 18 can have same birth month?

This is not a class assignment. It so happened that 4 team members in my group of 18 happened to share same birth month. Lets say June. . What are the chances that this could happen. I'm trying to ...
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### Calculating the probability of duplication in a random number sample

If I sample 23 random numbers from 1-365, how could I calculate the probability of there being a duplicate? Context to this question: I was looking into the birthday paradox and I wanted to explore ...
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### Proper length of random nonce for hash calculation (blockchain)?

I have a string s and I need to calculate a nonce such that when appending the nonce to the string, the generated hash starts with a given sequence. The hash has 256 bits, so the number of ...
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### Acronyms duplicates (a generalisation of the birthday problem)

I brought more precision into the way I ask this question to make it investigatable: Assume that everyone has a First name, a Family name, a Street name and a Suburb name. If you make a four-letter ...
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### Reverse birthday problem with multiple collisions

Assume you had an alien year with an unknown length N. If you have a random sample of said aliens and some of them share birthdays, can you use this data to estimate the length of the year? For ...
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### A reverse birthday problem: no pair out of 1 million aliens shares a birthday; what is their year length?

Assume a planet with a very very long year of $N$ days. There are 1 million aliens at a party in a room, and no one at all shares a birthday. What can be inferred about the size of $N$? (This more ...
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### Is this a reverse Birthday Problem problem? [duplicate]

I have a machine that generates 16 character long sentences made up of (I think kinda) random letters. I can get it to spit out up to 1 million such sentences before I loose the ability to store them (...
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### Sampling pairs without replacement from two urns with overlapping populations

I have been trying to derive the coefficient of inbreeding lately, but I am at a loss. If I understand correctly it measures the probability of an allele "collision" i.e. getting the same allele from ...
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### Efficient random generation for generalized birthday paradox problem?

In generalized birthday paradox problem The probability of getting $k$ unique values from $[0, n)$ when choosing $m$ times is given by: P(V = k) = \binom{n}{k}\displaystyle\sum_{i=0}^k (-1)...
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### number of different events in a random sequence

I'm confronted with a probability problem that may have already been solved. I'm considering random sequences of m events. The number of possible events is n, and each type of event has the same ...
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### Sample space and outcome of birthday problem

Suppose, calculating the probability of having at least two peoples same birthday from 25 people. What is the sample space and outcome of the experiment? As far as I pondered, S = 365^25 and outcome ...
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### Birthday problem independent events?

The Wikipedia article about the birthday problem explain how to calculate the probability of birthday collision. They're simply telling in the process that the events are independent : When events ...
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### Probability of last 3 digits matching in 9 digit student ID

Here is the scenario: There are a number of students (n), each with a random 9-digit integer student ID number (including zeros). At what n-value would there be a 0.5 probability at least two ...
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### Birthday Problem: Difference between Canonical Solution and Approximation

A couple weeks back, I was seeing if I could solve the basic formulation of the Birthday Problem (i.e. assuming 365 equally likely birthdays, what's the probability that, given a room of ${n}$ people, ...
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### How many identical pairs in a random draw?

I have an infinite stream of good random numbers available to me that range 0 - 255. I draw them in pairs. In how many pairs will both numbers be equal? I think that this is a form of Birthday ...
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### What's the expected number of distinct values within a binomial distribution sample?

Given $X$ has a binomial distribution $B(n,p)$. Now I take $k$ samples from $X$. What's the expected value of how many distinct values I sampled? My rather futile approach was: Given after $k$ draws, ...
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### Birthday Paradox: does it count if people are born in the same year?

Does the birthday problem change if we only take people from the same year (e.g. a classroom)? Intuitively I think it does, because you have more probabilities to have two people born in different ...
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### Just curious of the odds of this happening

Was having lunch with a lover on the boardwalk and he pulled a random couple off of the boardwalk to have lunch with us. As we were talking, we discovered that both men had the same birthday, and the ...
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### Poker and the Birthday Problem

The number of possible poker hands drawn from a standard 5-card deck is ${52 \choose 5}$. This is sampling without replacement where order does not matter, e.g., ...
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### Birthday paradox, two generations, different continents [closed]

I have been reading about the birthday paradox & was trying to take it further & apply it to an example from my own life:- I am a Brit married to an American. My British sister-in-law shares ...
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### Birthday "Paradox" -- with a different perspective

Background: Many people are familiar with the so-called Birthday "Paradox" that, in a room of 23 people, there is a better than 50/50 chance that two of them will share the same birthday. In its more ...
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### Birthday paradox with a (huge) twist: Probability of sharing exact same date of birth with partner?

I share the same birthdate as my boyfriend, same date but also same year, our births are seperated by merely 5 hours or so. I know that the chances of meeting someone who was born on the same date ...
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### What is the probability that a person will die on their birthday?

I am curious about what the probability is that a person will die on their birthday? I am sure there are a number of ways to approach this, plus I have heard that actual numbers point to a higher ...
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### Expected number of duplicates (triplicates etc) when drawing with replacement

I have the following problem: I have 100 unique items (n), and I'm selecting 43 (m) of them one at a time (with replacement). I need to solve for the expected number of uniques (only selected once, ...
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### Birthday problem, but matching couples instead of individuals

Suppose n couples are invited to a party. What is the probability that there are at least two husband–wife pairs such that the husbands have the same birthdays and so do their wives?
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### Calculating the probability of the Nth sample in the birthday problem w/o knowing the previous samples

If we draw two random variates from a discrete uniform distribution $[1, D]$, the probability that the samples are distinct is $(D-1)/D$. Explanations of the birthday problem state that if we sample a ...
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### Probability of Unique Minimum (Discrete)

This is a discrete problem concerning integers. If there are $n$ independent random variables $X_1,...,X_n$ that each take on a value from $\{1,...,x\}$ uniformly at random ($x$ distinct values), ...
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### The Birthday Problem, revisited...?

I'm currently facing a problem I have been stuck in for almost half a day and I really can't keep this because I have a lot of work to do! It obviously has to do with the birthday problem. The ...
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### What is the real answer to the Birthday question?

"How large must a class be to make the probability of finding two people with the same birthday at least 50%?" I have 360 friends on facebook, and, as expected, the distribution of their birthdays is ...
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In the traditional Birthday Paradox the question is "what are the chances that two or more people in a group of $n$ people share a birthday". I'm stuck on a problem which is an extension of this. ...