Linked Questions
21 questions linked to/from Probability of 3 people in a room of 30 having the same birthday
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Is there a generalized solution to the birthday problem? [duplicate]
The problem of the calculating the probability that there is a birthday shared by at least 2 people in a group of size n is well known. I am wondering if there is a way of finding the probability of ...
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What is the probability that at least 3 people have the same birthday in the same year [duplicate]
Consider a group of size 40. What is the probability that at least three
members of the group were born in the same month and in the same day (same birthday)?
Ignoring leap years.
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Birthday paradox with M shared birthdays [duplicate]
Possible Duplicate:
Probability of 3 people in a room of 30 having the same birthday
The birthday paradox is a common problem about the probability that any 2 people from a random set of $N$ ...
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What's the probability that 3 out of 23 people will share the same birthday? [duplicate]
The probability that 2 out of 23 people will share the same birthday is slightly higher than 50%, and that is the famous Birthday Paradox. However, what is the probability that 3 out of 23 people will?...
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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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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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Birthday Problem applied to collisions
I'm trying to extend the birthday problem to detect collision probability in a hashing scheme. Here is my problem. I use the letters and numbers [A-Z][a-z][0-9] to make a set of keys by randomly ...
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What is the probability that throwing $m$ balls at random in $n$ urns at least one urn contains $c$ elements?
Let us fix a number of urns $n$ and a fixed capacity $c$. I would like to know which is the probability that $m$ balls, thrown at random in $n$ urns, "overflow", in the sense that at least one urn has ...
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Probability of at least 3 people sharing a common birthday
What is the probability that 3 or more people share a common birthday, in a group of 160 people?
Approach:
We have:
$P(X\geq 3)= 1-[P(X=0)+P(X=2)]$.
(where $X\geq i$ means at least $i$ people share a ...
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What's the probability of getting any one face at least $m$ times, when throwing a $k$-sided die $n$ times?
Say we have a $k$-sided die, and we want to throw it $n$ times.
What's the expression for the probability of getting any one face up at least $m$ times, where $m \in \{0, ... , n\}$?
Edit: The ...
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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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how many persons need to be in one room , so AT LEAST 3 people have the same Birth MONTH?
how many persons need to be in one room , so AT LEAST 3 people have the same Birth MONTH ?
Another Answer i suggest : (correct me if i'm wrong) there should be 15 People at least , because if there's ...
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Birthday problem extension question
I have N balls and M boxes. The balls are thrown at random onto the boxes. What is the probability that some box contains at least 3 balls?
Based on the Birthday problem, I know how to find the ...
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Birthday paradox problem in terms of months
Question -
Consider the following-
It is equi-probable to have a birthday in any month of the year.
6 random people are put into a room.
Q1. Find the probability that at least two people have a ...
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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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Expected maximum number of simultaneous celebrators
Suppose there's a set of 500 individuals. What is the expected number of coinciding birthday celebrators? That's easy - it's $500/365$, under the assumption of uniform distribution.
But a birthday ...
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A question about combination
Here is the question:
Let $k,m,n$ be positive integers and $k\leq m\leq n$.
Compute
$$\sum_{\substack{a_1+\dots+a_n=m,\\ 0\leq a_i<k, \text{for } i=1,2,\ldots,n}}\frac{m!}{a_1!a_2!\cdots a_n!}...
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Probability of $X$ collisions on random selections from pool
I have a bag of $100$ marbles. I draw a marble at random and put it back in the bag. I do this a total of $50$ times. What is the probability that there is at least one marble which I picked at least $...
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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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Probability that the maximum number of dice with the same face is k
Let say we have $N$ dice with 6 faces. I'm asking my self, what is the probability that the maximum number of dice with the same face is $k$?
In more precise terms, what is the size of this set?
\...
