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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Unknown distribution for birthday problem
Coming from Blitzstein's book:
In the birthday problem, we assumed that all 365 days of the year are
equally likely (and excluded February 29). In reality, some days are
slightly more likely as ...
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Family Members Birthday Dates all different, but our birthdays will fall on same day, even Leap Years. There is a total of 9 in this Birthday Club. .
I can compile a list if needed and post, but I noticed this over 50 years ago, My Father, My Brother and Myself our Birthdays fall on the same day of the week every year. Even Leap years, that does ...
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Birthday Problem: Confusion between PMF and CDF -
The question:
(Introduction to Probability, Blitzstein and Nwang, p.128)
People are arriving at a party one at a time. While waiting for more
people to arrive they entertain themselves by comparing ...
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How many people must be in a room until it is at least a $50\%$ chance that two will have the same amount of change?
Book problem: If the amount of change in a pocket is assumed to be uniformly distributed from $0$ to $99$ cents, how many people must be in a room until it is at least a $50\%$ chance that two will ...
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The Birthday paradox with variable-likelihood birthdays. [duplicate]
I know that the Birthday Paradox is the fact that in a room of 23 people, the chances are more than 50 percent that at least two people share a birthday. However, this is under the assumption that all ...
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Birthday Problem Confusion Using the Counting Rule
I am stumped by the below confusion:
Question: How many people do we need in a class to make the probability that (at least) two people have the same birthday more than 1/2? (For simplicity, assume ...
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Number of date collisions in birthday problem
If I generate uniform random integers from 1 to K and count how many unique numbers I get $n_\mathrm{unique}$, I empirically obtain:
the mean is: $\frac{2K}{\pi}$
the variance is $\frac{K}{\pi^{2}}$.
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How can I prove that the probability that exactly 2 people share the same birthday is more likely than everyone has a different day out of 20 people? [closed]
I will be thankful if you can help me and show how to solve this.
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Miscalculating Probability of At Least $2$ People Having The Same Birthday
Regarding the problem: choosing 23 people randomly, show that there is greater than a $50$ percent chance that at least two of them will have the same birthday. What is the error in the way I'm trying ...
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Classmate birthday Probability [duplicate]
I dealt with one issue, namely:
Consider $k$ independent realizations of a random variable uniformly distributed over a set of $n$ values.
1 What must $k$ be for the probability that the given outcome ...
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Birthday-esque problem, but for 2 pairs, or a triple
Let's say I've got a pool of 20 numbers, and each event chooses a number randomly. I'm trying to find the 50% point for one of these three:
50% chance that by this event, at least 1 duplicate number ...
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Help with deriving solution for multiple birthday problem
I've been thinking about one version of the more general birthday problem, namely for the case of k $\ge$ 3. I found this document explaining the solution through a combinatorial method, but I'm ...
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How to work out the probability of two random sequences sharing a certain number of matches?
Pick two sequences of numbers, $S_1$ and $S_2$. $S_1$ is $n_1$ picks from $1$ to $k$, $S_2$ is $n_2$ picks from $1$ to $k$. There could be duplicates within each sequence, for instance $S_1$ might ...
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Collisions in a Sample [closed]
Based on birthday paradox;
Let $d$ be the set of elements randomly chosen from a set of $n$ distinct elements then
a) What is expected number of unique elements in $d$ (remaining will be repetition of ...
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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?
Suppose we sample uniformly random elements from a set of cardinality $n$, and save them in a table. We continue doing this process (each sampling is one step) until we get a collision. What is the ...
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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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Figuring out N = 23 Birthday Problem - Probability
I am incredibly frustrated so please excuse me.
I know I can just run the computations but I am struggling to figure out algebraically how I can figure out that n = 23 whereby it takes a minimum of 23 ...
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Birthday Problem: Justify Why $n$ is Greater Than $\frac{365}{2}$
Problem (skip to part d): Ignoring leap days, the days of the year can be numbered $1$ to $365$. Assume that birthdays
are equally likely to fall on any day of the year. Consider a group of $n$ people,...
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Birthday Problem: Finding a Probability Function of an Event
Problem: Ignoring leap days, the days of the year can be numbered $1$ to $365$. Assume that birthdays
are equally likely to fall on any day of the year. Consider a group of $n$ people, of which
you ...
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What is the probability that three living people in the same family will celebrate their birthdays on exactly the same day.
I celebrate my birthday on the same day as one of my grandchildren. Just wonder how rare it would be for three people in the same family to celebrate their birthdays on the same day.
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Progressive Birthday problem
The Birthday Problem is very interesting to me. The more dates you fill up, the lower the chances a date will be outside what has already been seen.
But I do not seem to understand at all how ...
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probability of 2 person has the same birthday in a class.
problem: there are n persons in a room, what is the probability that no two of them celebrate the same birthday in a year?
Here is my thought process,
The sample space is $|\{(b_1,b_2,\dots,b_n): b_1,...
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Probability of no birthdays for X consecutive days within a group of n people
Consider a group of n people. Assume 365 days in a year and that birthdays are independent and uniformly distributed.
What is the probably that ...
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What is the expectation value of the minimum 'distance' between two random 64-bit numbers out of a set of N?
Assume we have a set of N random integer numbers in the interval [0, 2^64> (or equivalent, consider N randomly chosen corners (vectors) of a 64-dimensional ...
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At least how many residents of the country have the same birthday?
I am trying to solve a pigeonhole question in discrete mathematics.
Let's suppose that a country has 11.000.000 people. At least how many residents of the country have the same birthday?
Take into ...
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What is the probability of at least one pair of people who share a birthday and whose mothers share a birthday?
Problem $71$ of Chapter 4 from Introduction to Probability by J. Blitzstein and J. Hwang.
In a group of $90$ kids, what is the approximate probability of there being at least one pair of kids born on ...
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Which would be the "direct" formula for the birthday paradox , withouth subtracting to 1?
I stumbled upon the birthday paradox, and I get it.
However, all the explanations I see solve the probability by subtracting to 1 the probability of all people having different birthdays. What I am ...
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Average number of birthdays today
On Facebook, I can see which friends have birthdays today. Sometimes there are 1, sometimes more than 1, and sometimes zero friends. What's the average number of birthdays today? To formalize:
Problem ...
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Find the probability that at least two people out of $k$ people will have the same birthday
The Birthday problem. Find the probability that at least two people out of $(k=5)$ people will have the same birthday.
The usual approach would be to use $$p=1-\frac{P_{365,5}}{365^5}$$
However, I ...
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Probability distribution for birthday paradox
In Wikipedia we read
In an alternative formulation of the birthday problem, one asks the average number of people required to find a pair with the same birthday. If we consider the probability ...
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Random Variable - Birthday Problem
How many people are needed so that the probability that at least two of them were born on the same day of the week is at least 1/2? (Assume that the days of the week are equally likely to be the ...
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A man invited five friends.
A man invited five friends. He was born in April as also all the invited friends. What is the probability that none of the friends was born on the same day of the month as the host?
The way I ...
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Birthday problem - expected number of shared birthdays
Given $m$ people and an $n$ possible "days of the year", what is the expected number of days which 2 or more people share as a birthday (if the distribution of birthdays is iid uniform over ...
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$1/2 = 1 - e^{-n(n-1)/2d}$ General Birthday Formula? [closed]
When solving $\frac{1}{2} = 1 - e^{-n(n-1)/2d}$ for $n$, the solution should be $n \approx \sqrt{\ln(4)d}$. But I can't get the calculations done.
Any advice would be highly appreciated.
Thank you!
...
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Birthday Problem as people enter in the room
On the wikipedia page regarding the birthday problem there are several variations to it:
https://en.wikipedia.org/wiki/Birthday_problem
One of the variations is this one:
as people enter a room one at ...
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Solving Birthday Paradox with Triangular Number formula
I have an incorrect solution to the classic birthday paradox question, and while plugging in some values shows the formula is wrong, I can't see any intuitive reasoning as to why it is incorrect, or ...
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How do you calculate the probability of *only* 2 people having different birthdays (excluding leap years)?
I know that the numerical answer is $\frac{364}{365}$, but I didn't understand why. this answer seems to contradict my current understanding of probability. For example, to calculate the probability ...
