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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Probability for channel collision

I have n=21 end devices, sharing c=3 radio channels for sending packets (assume, they try it time synchronously) Actually, I want to know, how many devices n_2 I can have, if there are c_2 = 7 radio ...
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Probability of 4 parents sharing 2 birthdays [closed]

I'm a math idiot and I'm trying to figure something out. My mother was born on April 10th as was my friend's mother. My father was born on July 4th as was my friend's father. How do I calculate the ...
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Probability- Birthday problem

The traditional way of finding the answer is to find the complement and subtract from one. I tried an alternative solution. I come up with a formula. for $k$ people, $P(k)=P(k-1)+{(k-1)\over365}\...
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Probability of birthday [closed]

In this years IMO a decision has been taken that each team will be consist of 10 members. What is the probability that at least two people will have a birthday on the same day of the week?
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At least 2 share the same birthday but without doing actual calculations for the probability

I am reading the following problem: If $20$ people are selected at random, find the probability that at least $2$ of them have the same birthday. As a follow up, how large a group is needed to give a ...
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closed form of multiple in the probability of a two to one collision problem (birthday paradox).

I have a problem where I need to find the chance of finding a collision in a two to one set of size $N$. For example: Let's say I have 10 indices. There are then 5 pairs that map to the same output. ...
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Birthday problem for people knowing each other

Suppose a large chat room for a country, what is the probability that two people know each other in real-life? We have: n: The number of people in the chat room d: The number of persons the average ...
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Show that in a group of four people it is more likely than not that two of them were born on the same day of the week. [closed]

I've started the working : Possible combinations : AB AC AD BC BD CD = 6 P(2 people born same day of week) = 1 - P(No people born on same day of week) =1−((7/7)⋅(6/7)⋅(5/7)⋅(4/7))=1−(120/343)=223/343≈...
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Unclear how to prove this logarithmic reduction of a sequence, in reference to the birthday problem

On page 46 of Rouse Ball and HSM Coxeter's Mathematical Recreations and Essays, 13th ed., appears this step, in reference to the birthday problem $$ (1-\frac{1}{365})(1-\frac{2}{365})...(1-\frac{n-1}{...
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Birthday Paradox with Leap Year

I looked online, and found more than one and inconsistent answers to the Birthday Paradox when we throw the leap year into the mix. None of the answers I saw match with my own. I am posting my ...
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Birthday Problem: Expected number of people in a room

If an infinite amount of people enter a room one by one, what is the expected number of people in the room when you first find two that share the same birthday? (Assuming no leap years and every ...
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Given a concrete day, probability that two people have birthday on the same day.

What is the probability that on a specific day (e.g. December 24) two people have birthday in a room with 23 people? The probability, given a specific day, one person has birthday is in my opinion $\...
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Calculation of probability that at least 2 out of n people have the same birthday leads to paradox

Usually, the way the probability that at least 1 pair out of n people have the same birthday is calculated is by calculating the probability of the converse statement - the probability that no pair ...
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Birthday probability question

I came across a variation of the birthday problem asking "in a room of $4$ people what is the probability that at least $3$ of them share the same birthday". I was unsure of the answer and ...
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Why is this solution for the birthday problem wrong?

How many people do you need in the same room for the probability $p$ to be at least $0.5$ for two people to have the same birthday? My idea is that for every pair of people the probability that their ...
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The Birthday Paradox with combinatorics

Assume a year has $365$ days, how many are required to have a $50%$ chance of $2$ people having the same birthday? According to Scientific American, there are $23$ people needed to achieve the goal. $$...
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Birthday Problem: Expected Number of people with common birthday [duplicate]

This might be a different variant of the typical birthday problem. Given a room of $n$ people, let $N$ be a random variable representing the number of people who have a birthday common with at least ...
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Birthday problem with large $n, d$ values

In the Birthday problem, the formulas $${\displaystyle {\begin{aligned}p(n;d)&={\begin{cases}1-\displaystyle \prod _{k=1}^{n-1}\left(1-{\frac {k}{d}}\right)&n\leq d\\1&n>d\end{cases}}&...
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My try of the Birthday Paradox

I have seen the solution of the paradox on Wikipedia, but before that I tried it out myself. But I got my answer wrong with my approach. To calculate the probability of no two people in a group of 23 ...
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Variation of Birthday problem - Group of n people

I know this has been posted several times and I have gone through most of the relevant posts. Here is one which I am having a difficult time to solve: There are 450 people in a room; (1) how many of ...
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Birthday problem (combinatorics), without using inverse solution

There is that classic question about how many people in a room is required so that at least one pair of people share a birthday, with > 50% probability, the answer is 23. The standard textbook ...
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Expected number of triples of friends

There are $n$ people are at a party. The probability that each pair of people is friends is $\frac{1}{2}$ (independent). Let $X$ be the number of triples of people that are friends. Find $E[X]$ For ...
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Expected value vs probability

Sorry in advance, it is probably a stupid question. I encountered it when I was thinking about the birthday problem. The probability of having at least one pair of the same birthday is $$ 1- \frac{365\...
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Probability of birthday chain

Let $B(k,n)$ be the probability that a consecutive birthday chain of length $k$ can be found in $n$ people, excluding leap days and assuming that December 31 and January 1 are consecutive. After some ...
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Birthday problem: solving with permutations vs combinations

I have a problem with an exercise: If k people are at a party, what is the probability that at least two of them have the same birthday? Suppose that there are n=365 days in a year and all days are ...
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Probability of having the same birthday without complement

I understand the probability of getting at least n amount of people.Assume 365 normal days But I would someone to check if my reasoning for this particular question is right ? I would like to know ...
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Growth rate of the expected number of draws with replacement from an urn with $n$ balls needed before you draw the same ball twice

Consider an urn with $n$ balls. Draw a ball from the urn and put it back. Repeat this until you draw a ball that you have drawn before. Let $E(n)$ denote the expected number of draws that result from ...
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What's the probability in a group of 8 people at least 2 people rolling the same number

In a group of 8 people what are the chances of at least 2 people getting the same number if they're rolling from 1 to 99 on a uniform distribution? I've tried working this out by finding out the ...
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Generalised Birthday Problem

How would I solve a generalised Birthday Problem? Like assume birthdays aren't uniformly distributed, instead are p(1), p(2), p(3) ... p(365). Of course for a more general solution it will go on till ...
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Question about Birthday Problem [duplicate]

My first intuition was to think $P(\{\text{No two bdays coincide}\}) = \displaystyle{\frac{\binom{365}{n}}{365}}$ given $365 \ge n$. Turns out $P(\{\text{No two bdays coincide}\}) = \displaystyle{\...
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Birthday paradox but up to X collisions are acceptable

I'm familiar with the basic version of the paradox: given a number of people, what is the probability that at least 2 people share the same birthday in a calendar year. However, I want to ask if there'...
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Probability that two non-twin siblings are born on same day

I want to compute this probability. I take the first sibling, mark their birthday, and then assume that the second siblings birthday is random, so I get that there is a 1/365 chance. Certainly there ...
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Birthday problem modified: Expected number of birthdays [closed]

Given there are N people in one room and let us assume that they are born randomly on one of x(=365) days in the year. What is the expected number of different birthdays for N people? Edit: I think ...
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Probability to calculate the birthday match [duplicate]

Is there any intuitive way to calculate the probability that in a randomly chosen group of r people at least three people have the same birthday
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Estimating number of people in a group based on knowing the number of birthdays for today

Lets say there is a group of people and we don't know how big is this group. Lets say that we are told that 3 people had a birthday today. For simplicity we can assume that birthdays are uniformly ...
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Birthday problem variant

There are $n$ people present in a room. Assume that people’s birthdays are equally likely to be on any day of the year. What is the probability that at least one of them celebrates their birthday on ...
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Combinatorics problem related to Birthday Problem from Introduction to Probability

Problem A group of 50 people are comparing their birthdays (as usual, assume their birthdays are independent, are not February 29, etc.). Find the expected number of days in the year on which at ...
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Directly Calculating Birthday Paradox Probabilites

I am trying to calculate the probability of at least 2 people sharing a birthday in a group of 4 people. I understand that calculating it as 1-P(no shared birthdays) is simpler, but I would like to ...
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(approximate) probability that all items in a multiset that is drawn with replacement have multiplicity $\geq k$.

This problem seems to be the following variation of the birthday problem: what is the probability that in a group of $p$ people nobody has a birthday that $<k$ people in the group have. I'm also ...
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344 views

How to calculate birthday problem for collisions of a random number generator

I'm creating a script that generates random numbers for invoices as fully described here. The current version of my script includes logic to prevent collisions, but this means that every time there is ...
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Birthday Problem Proof?

I was looking at the Birthday Problem (the probability that at least 2 people in a group of n people will share a birthday) and I came up with a different solution and was wondering if it was valid as ...
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Birthday Problem: Probability that at least two also share the same weekday, if weekday uniformly distributed and independent of birth date?

Consider the following problem extension for the birthday problem: We now want know the probability that out of $n$ persons, at least two people were born on the same date and the same weekday (for ...
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Probability distribution for collisions / birthday problem

Let's say I have a source of randomly produced values from a range $M$. I want to test if the source is a uniform distribution by examining a sample sequence of $n$ values $m_1, m_2,\dots,m_n$. ...
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Is this like the Birthday Problem? Poisson Halloween Party

Suppose that there are n guests at a Halloween party, and that each is wearing one of 200 possible costumes available at local store, uniformly at random and independently of all other guests. Using ...
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Find $n$ such that $365 \left(1-\left(\frac{364}{365}\right)^n - n\frac{364^{n-1}}{365^n} \right) > 1$

I need to find $n$ such that $365 \left(1-\left(\frac{364}{365}\right)^n - n\frac{364^{n-1}}{365^n} \right) > 1$. The answer is $n \ge 28$. Expanding the equation out, rearranging it, taking ...
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Birthday Paradox from different perspectives

When there’s 23 people in a group, the chances that 2 or more people have the same birthday is: $1-\bigl(\frac{364}{365}\bigr)^{253}\approx0.5005$ which is found by taking the chances that a pair ...
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Estimate the probability that N random 4-digit pin numbers are all distinct for N=10, 1000, 100

As per title, the question is "estimate the probability that N random 4-digit pin numbers are all distinct for N=10, 1000, 100". My current working is as follows: There are $10^{4}$ total 0-10 4 ...
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Birthday paradox question

I am solving the question: How large must a class be to make the probability of finding two people with the same birthday at least 50%? The first solution I came up with is rather simple. It's based ...
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Probability that $n$ persons share their birthdays on exactly/at most $k < n$ months?

I have two exercises. What is the probability that $n$ independent persons share their birthdays on exactly $k<n$ months? What is the probability that $n$ independent persons share their ...
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Expected number of hash insertions until next collision

Other questions like this start with an empty hash, and look for the expected number of hash insertions until the probability of a collision is 0.5. I'm starting off with a hash with existing keys, ...

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