# 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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### 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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### 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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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 ...
### 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 ...