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Questions tagged [birthday-paradox]

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.

The birthday problem or birthday paradox is a famous problem in combinatorics and probability theory. The problem is often stated as follows:

Suppose there is a classroom full of people. What is the probability that there are two people with the same birthday? How many people does there need to be in the classroom, so that the probability that two people share the same birthday is 50%?

For a popular introduction see the article Probability and the Birthday Paradox in Scientific American.

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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 than me is fairly high and I know a few people with…
curious
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Extending the birthday paradox to more than 2 people

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. Instead of knowing the probability that two people…
Simon Andrews
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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 present this as a probability problem in our team…
forecaster
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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 not uniform at all. I have one day with that has…
Adam
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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, k = 1), doubles (selected exactly twice k = 2),…
Kaitlyn K
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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 compact question supersedes this poorly phrased…
Paul Uszak
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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 function call is independent from each other and carries no state. I use this to generate X numbers; let's say these…
Taako
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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 example, in a sample of 100, you could have two…
Techhead
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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 $65536$ bins, with $M>N$, is there a way to do a…
Mini Fridge
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How many Americans, randomly chosen, are needed to have a 50% chance two live in the same or adjacent states?

Background I'm studying common coincidences and "near" coincidences that nevertheless (unduly) impress the average person. The below question is an extension of the famous Birthday problem, which asks "How many people, randomly chosen, are needed…
David G. Stork
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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 general form for n people, the probability of no…
TonyMorland
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Statistical equivalence in the birthday paradox

I was reading a Wikipedia article on the birthday paradox and stumbled upon the following statement: ...the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently... Could you explain what does it mean…
vitaut
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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 rate on birthdays, hence why I am asking it here.
jbranchaud
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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 allocated at random to $d$ bins. What is the greatest…
significance
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Birthday Problem: How am I wrong?

Before reading the Wikipedia article, my idea to calculate the probability was as follows: $1-\left(\frac{364}{365}\right)^{_nC_{2}}$ Basically, I thought to compare all combinations of pairs ($_nC_{2}$) and require them to have different birthday…
packet0
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