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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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What is the probability that in a group of n people chosen at random, there are at least two born in the same month of the year?

So I'm working on a probability problem: In Exercise 19 assume it is equally likely that a person is born in any given month of the year. b) What is the probability that in a group of $n$ ...
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Same birthday for two people with and without replacement

It is known that for choosing 2 people out of n with birthdays A,B the probability that A=B is $\frac{1}{365}$. In this case we have replacement which means that we may choose the same person twice. A ...
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Probability 33 people in a group of 100,000 have the same birthday? Assuming years have 365,000 days.

Probability 33 people in a group of 100,000 have the same birthday? Assuming years have 365,000 days. Would this Poisson Formula work? Updated! Note to OP: Probability of exactly $33$ people have ...
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how many persons need to be in one room , so AT LEAST 3 people have the same Birth MONTH?

how many persons need to be in one room , so AT LEAST 3 people have the same Birth MONTH ? Another Answer i suggest : (correct me if i'm wrong) there should be 15 People at least , because if there's ...
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What is the probability that two people's birthdays are always on the same day of the week?

This is related to the Doomsday rule. Certain days of the year, such as 4/4 and 6/6 are always on the same day of the week as each other in a given year. A first approximation would be $\frac17$. ...
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Probability of match in three elements choosing from a group

One of my teachers asked all 26 ($t$) of the students in our class to randomly choose 5 ($k$) exercises from a website from a set of 20 ($n$). He then said that no two students in the class should ...
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Repeated trials of the birthday paradox, plus

If: There are 32,768 possible dates in a year (instead of 365) and people have a completely uniform random distribution of birthdays. In each room there will be 3 people (if easy enough, alternate 3, ...
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Birthday paradox for large numbers

I'm attempting to test the claim: "Every card deck shuffled is unique. A shuffled deck of cards will exist once and never again." Assumption: A perfect world where a deck of cards is perfectly ...
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Distribution for count of unique elements

Consider the selection, with replacement, of $N$ elements uniformly at random from $\{1, 2,\dots, M\}$. From the selected elements, count the number of unique elements. Does the distribution of this ...
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What do Gegenbauer polynomials have to do with the birthday problem?

I was reading up on Gegenbauer polynomials for a blog post about the kissing number problem, which I also asked a separate question about later. On the Wolfram MathWorld plot summary for Gegenbauer ...
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$100$ persons think of a number between $1$ and $4900$. Probabilty: Thinking of same number vs. $1$ number chosen by multiple people

$100$ persons think independently of a number between $1$ and $4900$. What is more likely? All people have thought of different numbers $(1)$ A number has been chosen by more persons $(2)$ It ...
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Birthday problem vs having N known non-duplicates and choosing one more

I understand the birthday problem from a basic level, but I'm curious how checking for a pair after every choice of N alters the probabilities. For example, assuming you want to choose N random ...
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Probability of at least $3$ people sharing the same birthday in a group of $n$ people

Disclaimer: I've seen posts with good answers for the case of "at least $2$ people", or "exactly $2$ people". Posts with "at least $k$ people" usually suppose that the mutual birthday is a fixed day (...
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Show that $p_{n} \geq 1- \exp{(-n(n-1)/730)}$

On the issue of the birthday paradox,Let $p_{n}$ be the probability that in a class of $n$ at least $2$ have a their birthdays on the same day (exclude $29$ Feb). Use the inequality $1-x \leq e^{-x}$ ...
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Birthday problem with $110$ people - need help fixing my approach to get the variance

Let $X$ be the number of distinct birthdays in a group of $110$ people (i.e., the number of days in a year such that at least one person in the group has that birthday). Under the usual assumptions (...
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Minimising the probability of two people having the same birthday?

I was asked a particularly weird question at an interview today: Suppose Alice and Bob live on a universe in which a year has $k$ days. What probability distribution of birthdays would you choose ...
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What's the error in this birthday-problem estimation?

Theorem. Choose $Q$ random natural numbers in the set $\{1,2, ..., M\}.$ The probability of getting at least one collision is $$P_C(Q) = 1 - \frac{M - (Q - 1)}{M} P_{\neg C}(Q-1).$$ Notation. By $...
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Why does my approach to the birthday problem(with 3 people) produce a wrong result?

I'm trying to calculate the probability that at least two people out of three have the same birthday (simplified Birthday Problem). I know that calculating it using the complementary event is easiest, ...
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Birthday problem inequality for a varying amount of people

I have been struggling with this one of exercises for a long time now. There are d = $4k^2$ days and 2k people $P_1$ , $P_2$ , . . . , $P_{2k}$. For each $i$ with $1 ≤ i ≤ 2k$, define the event $B_i$...
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Odds of Two People having one DOB and another two people having a different DOB in a Group [duplicate]

So the odds of in a room of 14, two people sharing a DOB, and another two people sharing another DOB is 4.97%. However, I cannot figure out how to get to 4.97%. I calculated it being 1.9% by doing ...
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Expected value of the number of days where k people share their birthdays

I am trying to find the expected value of the number of days where exactly $k$ people have a birthday in a class which consists of $60$ independently chosen people. For $k = 0, 1, 2, 3, 4$ I am ...
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Generalized Birthday Problem? Combinatorics

I am having a difficult time understanding how to think about and analyze the following problem: (I have done research, but I am not sure how to phrase my enquiries and my research seems to be almost ...
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Expected number of slots required for channel access - Birthday paradox

Let $n$ be the number of users who want to access a channel divided into with $s$ time-slots and let $n<<s$. Each user randomly chooses one time-slot (out of $s$) for accessing the channel. A ...
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Percentage of 2 different Sets of Birthday Out of 14 People

I am trying to calculate the odds of in a group of 14 people, the percentage of there being 2 different birthday matches (2 people having one Date of Birth, then another 2 people having a different ...
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Birthday problem with limited bucket size

Let's say there are 1095 balls, 23 of them are black. Randomly assign each ball into 365 buckets, each has a maximum capacity of 3 balls. What is the probability of at least one bucket having at least ...
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Stuck on this birthday problem

Assume for simplicity that N people, all born in April (a month of 30 days), are collected in a room Consider the event of at least two people in the room being born on the same date of the month, ...
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Birthday problem - Asymtotic of MEAN number of uniform draws before collision

An experiment draws values uniformly at random among $k\ge1$, and stops when it is drawn a value identical to a previous one. The experiment's outcome $n$ is the number of draws before collision, an ...
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How many people do we need so that the probability of someone having the same birthday as Person A is 100%?

Suppose you have some designated Person A. How many people do we need so that the probability that one of those people has the same birthday as person A is 100%? The first thing that came to my mind ...
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the birthday paradox for $p=0.5$

What is the minimum number of people such that the probability for some of them to have a common birthday is $\frac{1}{2}$? So looking at the problem as "balls and bins". We have $n = 365$ bins and $...
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Birthday Problem in Continuous time

I encountered a practical problem and want a help (my Google skill fail T^T). Basically, this is a birthday problem in continuous space, is it hard to solve? Problem Statement ...
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Alternative way to solve complement probability?

Four people are chosen at random. What is the probability that: No two of them have their birthday in the same month? The first and second people chosen have their birthdays in the same ...
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how many people for a 50% of two or more have the same sign? [closed]

there are 12 signs of zodiac. how many people must be present for there to be at least a 50% chance that two or more of them were born under the same sign. im not sure what formula i should be using ...
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“reverse birthday problem” - inferring days in the year from collisions in sample [duplicate]

Say you have n randomly selected students from another planet whose birthdays are known. x of them have birthdays that collide with at least one other student. How do you estimate the number of days ...
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Question regarding Birthday Paradox

If there are 100 people in a room then what is the probability that at least 2 of them share birthdays? I read that answer should be $1-\left(\frac{365!}{265!\times365^{100}} \right)$, and I ...
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Birthday problem: using $^nC_r$.

In birthday problem say total number of people n < 365, then probability of all person having distinct birthday is given by, $$\frac{\text{total no. of ways of selecting $n$ numbers from $365$ ...
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Birthday Paradox Application

I learned about the birthday paradox or birthday problem in school, and it was pretty intriguing. I finished all my homework for said class but I am stuck one specific question, which is supposed to ...
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Days required to collide at least one hash? [closed]

Sorry I am new here and learning mathematics and cryptographic problems. Assume an hash algorithm is collision resistant like SHA256, and the hash value is 64bit in length, (2^{64} possibilities) ...
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Birthday Paradox: 4 people What is the probability that two (or more) of them have the same birthday?

Four people around a room. What is the probability that two (or more) of them have the same birthday? However, I am not sure if my working out assume finds out about the 2 or more part. I am using ...
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Independent Probability | Duplicate numbers

$11$ numbers between $1$ and $40$ are select. What is the probability there are some duplicated integers in those $11$? I think the answer to this question is very straightforward: $1-P(\text{they ...
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I live with ten people at a time. How many total housemates should I have gone through to expect that two of my housemates would share a birthday?

I live in a house with ten people. I've had about 50 people live here since I moved in. Nobody has ever shared the same birthday before, but a new housemate shares a birthday with a current housemate. ...
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Birthday attacks vs. Preimage attacks

I am trying to understand why a preimage attack is different than a birthday attack. Following the general description from Wikipedia (sorry if that is a poor source?): A preimage attack is where an ...
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Birthday problem- Adam and Eve

Question: Adam and Eve are in a room with $n − 2$ other people. Suppose you know that at least two of the people in the room celebrate their birthday on the same day. What is the probability that ...
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Calculating probability of no hash collision

Given a 64-bit hash function that takes arbitrary inputs, what is the probability that feeding 10 million inputs into the hash function will outputs 10 million unique outputs. I've came up with this: $...
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Computing Conditional Probability on Birthday Problem

I have a question concerning the birthday problem in conditional problem. Say there's a given group of $12$ people and a regular year with only $365$ days. Then the probability of no duplicate will be ...
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Birthday Problem: Finding the Probability Three People Have the Same Birthday

all. I'm working on the following probability problem. Birthday problems: 50 randomly selected students end up in a class, 365 days in a year. Find P for the following events. -i- A is the ...
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Birthday probability of $k$ people and $n$ days a year such that at least $2$ people have the same bday

A certain planet has n days in one year. What is the probability that among $k$ people on that planet there are (at least) two who share their birthday? My answer to this practice question is: There ...
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Birthday Problem Alteration

The well-known birthday problem asks how many people must be in a room before the probability of two or more people people sharing a (any) birthday is $>0.5$ and the answer is 23; a common ...
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Birthday Paradox Answer

I understand that if there are 253 comparisons to be made when checking if any two people out of 23 share the same birthday, that it's 1 minus the probability of them not sharing a birthday (.99726) ...
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Generalized variation of birthday problem: k-wise collisions for particular person

In a room with n other people what is the expected value of n for k other people to share the same birthday as me? I know from this very helpful wikipedia article that the probability for $k=1$ can ...
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Number of repetitions before collision (linked to but not exactly Birthday Problem)

There are $M$ persons in a room, and each one has chosen a random integer in $[1, N]$ (here $M$ much smaller than $N$). Now I repeat the experience of randomly choosing a number in $[1, N]$ and ...