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.

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 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 of 3 people in a room of 30 having the same birthday

I have been looking at the birthday problem (http://en.wikipedia.org/wiki/Birthday_problem) and I am trying to figure out what the probability of 3 people sharing a birthday in a room of 30 people is. (Instead of 2). I thought I understood the…
irl_irl
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Guessing the length of a playlist on "shuffle random?"

The other night I was hanging out with some friends and someone put on a playlist on shuffle random, where the songs are drawn uniformly at random from a fixed playlist. The person who put the playlist together forgot how many songs were in it, so…
templatetypedef
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birthday problem - expected number of collisions

There are many descriptions of the "birthday problem" on this site — the problem of finding the probability that in a group of $n$ people there will be any (= at least 2) sharing a birthday. I am wondering how to find instead the expected number of…
brannerchinese
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Group of $r$ people at least three people have the same birthday?

What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday? $\displaystyle 1- \frac{365\cdot364 \cdots(365-r+1)}{365^r}$ $\displaystyle \frac{365\cdot364 \cdots(365-r+1)}{365^r}…
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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 Adam and Eve celebrate their birthday on the same…
mrnobody
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Hyper Birthday Paradox?

There are $N$ buckets. Each second we add one new ball to a random bucket - so at $t=k$, there are a total of $k$ balls collectively in the buckets. At $t=1$, we expect that at least one bucket contains one ball. At $t=\sqrt{2N\ln{2}}$, due to…
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How can I solve bins-and-balls problems?

Below is the problem that I wanted to solve When there are $m$ balls and $n$ bins, balls are thrown into bins where each ball is thrown into a bin uniformly at random. What is the expected number of bins that contain strictly more than 1…
John
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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 solution to see if it is correct, or if I am missing…
jgsmath
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Classic birthday problem turned on its head: With $N$ people, how many are likely to share most common birthday?

I have a unique opportunity to present to a very large group of people ($2{,}000$ in a theatre hall) about how chance works and how human intuition can be way off to guess likeliness. Rather than present the classic birthday problem to them (that…
Benny Lewis
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How many expected people needed until 3 share a birthday?

I asked a somewhat related question recently and then became interested in this one: how many people are required, on average, until 3 share a birthday? More generally, if we have $M$ bins, what is the expected number of balls we must toss before…
Fixee
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Solution conflict: Expected number of distinct birthdays for $100$ people

I was given a homework question that is stated in the title. Although I have a conflict with the solution provided, and was wondering if you could help me understand why the solution is correct or if it is indeed incorrect. Define $X$ to be number…
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An extension of the birthday problem

Th birthday problem (or paradox) has been done in many way, with around a dozen thread only on math.stackexchange. The way it is expressed is usually the following: "Let us take $n$ people "independently" (no twins, etc.). What is the probability…
D. Thomine
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Probability question (Birthday problem)

I was wondering if someone could critique my argument here. The problem is to find the probability where exactly 2 people in a room full of 23 people share the same birthday. My argument is that there are 23 choose 2 ways times $\displaystyle…
Low Scores
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Birthday "Paradox" - another, different, version!

Background Many people are familiar with the so-called Birthday "Paradox" that, in a room of $23$ people, there is a better than $50/50$ chance that two of them will share the same birthday. In its more general form for $n$ people, the probability…
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Probability of Multiple Collisions in the Birthday Problem

I need help with an approximation concerning the birthday problem. In a recent MAA Monthly (August-September 2013) article "Simple Approximation Formulas for the Birthday Problem" by Matthias Arnold and Werner Glass, the authors claim the…
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