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 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. ...
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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 ...
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Variance of time to find first duplicate
In repeated uniform sampling from $\{1,\dots,n\}$ the mean time $E(X)$ to find the first duplicate is asymptotically $\sqrt{n\pi/2}$. What about the variance?
The variance is $E(X^2) -E(X)^2$.
$...
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birthday problem - which solution for expected value of collisions is correct?
I am trying to understand the difference of the two solutions for the expected value of collisions for the birthday problem:
https://math.stackexchange.com/a/35798/254705 derives the following ...
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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 ...
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Explain the Birthday Paradox
I recently read about the Birthday Paradox which states that in a group of 23 people, there's a probability of 50% that 2 people share their birthday, probability wise.
I calculated and don't think ...
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probability question ("birthday paradox")
$n$ people attend the same meeting, what is the chance that two people share the same birthday? Given the first $b$ birthdays, the probability the next person doesn't share a birthday with any that ...
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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 ...
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Birthday Probability
In my daughter's class of $23$, three students and the teacher all share the same birthday. Of course, there are $365$ days in the year, and the first case of the shared birthday is not counted in the ...
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Understanding the "Birthday Problem"
I found on this website http://www.cut-the-knot.org/do_you_know/coincidence.shtml proof that the probability of two people in a room having the same birthday equates to 50% when when there are 23 ...
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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{...
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Birthday Problem for 3 people
I know that, in a room of 23 people, there is a 50-50 chance that two people have the same birthday. However, what I want to know is: How many people do you need to have a 50-50 chance that 3 people ...
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Probability of exactly two pairs share a birthday, and each pair shares different birthday
This isn't for homework, just a thought.
Let's say there are $n$ people where $n \leq 365$ (I'm not entirely sure how to approach the problem if $n > 365$ and inquire about that down below). What ...
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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 ...
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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 ...
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