# 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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### 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 ...
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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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### Birthday Problem: Expected Number of Birthdays

For a group of $130$ people, assuming that each person is equally likely to have a birthday on each of $365$ days in the year, compute a) the expected number of days of the year that are birthdays of ...
38 views

So I saw this interesting problem: https://en.wikipedia.org/wiki/Birthday_problem And I am not the best at probability, so my question is why I cant calculate the probability with P (2 in n same ...
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### Probability Two People are Born on the Same Date (alternative way)

What is the probability two people (individuals) will have the same exact birthday? There are 365 days in a year and I assume that any person can be born on any random day, so uniformly. I like to ...
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### Trying to solve the card shuffle and birthday paradox question

I'm trying to solve the question as to whether two 52 card shuffles have ever been the same but I can't calculate the final step. Additionally I can't find any answer on the internet that has ...
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### Probability that N people have the same birthday [duplicate]

This question is from the book "Heard on the Street." There are N = 25 people at a party. One person asks everybody to announce their birthdays and for anyone who has the same birthday as someone ...
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### 400 people are in a room. What is the probability of two random people having the same birthday? [duplicate]

There are 400 people in a room. I pick two people at random. What is the probability that they have the same birthday? I know that there must be two people in the room who share the same birthday ...
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### Probability problem, a variant of the birthday problem

There are $m$ bins and $n$ identical balls. We randomly (uniformly) throw the balls to the bins. Then we count the number of bins which only have 1 ball in it. What is the probability that this number ...
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### There are 3 people in a room.What is the probability atleast 2 of them share same birthday

I want to know how to solve by NAIVE APPROACH, NOT by taking complement. That is, not by calculating the probability that no one shares a birthday and subtracting from 1 to get the answer.
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### Two solutions to two people having the same birthday

I came across the birthday problem on a forum and I found that there were two answers. My knowledge of probability is pretty limited so I can't quite understand the difference. X and Y having the ...
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### Variation on Birthday Paradox Problem

So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people’s birthdays are ...
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### Birthday problem: By symmetry, the variance is $\text{Var}(X) = 365 \text{Var}(I_1) + 2 {365 \choose 2} \text{Cov}(I_1, I_2)$.

I have the following problem: 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). ...
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### Birthday problem: $X = \sum_{j = 1}^{365}$ with $I_j \sim \text{Bern}(p)$ where $p = 1−(364/365)^{110}$

I have the following problem: 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). ...