Questions tagged [birthday-paradox]
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.
50
questions
21
votes
2
answers
4k
views
How many numbers can I generate and be 90% sure that there are no duplicates?
Suppose I am generating random 4-digit numbers. Obviously there are 10,000 possible numbers, but the chances are I will get a duplicate long before I generate that many.
Can anyone explain how I would ...
- 885
6
votes
1
answer
184
views
Birthday paradox for non-uniform probabilities
Suppose we take draw $k$ IID samples from multinomial distribution
$$\mathbf{p}=p_1,p_2,\ldots,p_d$$
What is the smallest $k$ such that probability of drawing the same class twice is at least 50%?
In ...
- 6,199
0
votes
0
answers
46
views
A variation on the birthday paradox
A question to the community:
Given N persons, and a period of M months, what is the probability at least one will have a birthday within the period?
P(bday in period) = N * (1/12) * (M/12)
This 'feels'...
- 1
10
votes
2
answers
676
views
How to determine the likelihood a random number generator is using a uniform distribution?
Let's say I have a blackbox function generate_number() that generates a random number between 1-N; and assume N is known. Each ...
- 203
3
votes
1
answer
100
views
Birthday puzzle
I need some help with Bayesian statistics likelihoods. Consider the following question: Given a number of persons. Each person $p$ knows $n(p)$ other persons – $p$'s neighbourhood $N(p)$. Knowing a ...
5
votes
2
answers
222
views
How do you find quantiles in this balls-in-bins problem?
I need to calculate the expected number of hash collisions with a range for a software project. I think this is a reformulation of the birthday problem, as follows.
Suppose you have $n$ balls ...
- 103
0
votes
0
answers
26
views
Calculate the minimum amount of student to be in a class for it to be more than 50% likely that two of them end up with the same ID digits
Question:
Suppose a professor assigns exam seating using the last 4 digits student's ID. How large
could a class be before it is more likely than not that at least two students will not be able to ...
1
vote
1
answer
784
views
Drawing a random sample without replacement from data set
I have data generated by a RCT with a control and treatment group, each with n=300, so N=600. The observations are assumed to be i.i.d..
From that population, I'd like to draw 5 random observations ...
8
votes
1
answer
480
views
Maximum Likelihood Estimator on birthday paradox
I am looking into some properties of some hash functions. It is rather a short hash $16bit$ which yields up to $65536$ different values.
Given that I have $M$ samples which populate $N$ out of $65536$...
- 145
3
votes
1
answer
158
views
Generalized birthday problem plus spouse
Suppose a group of persons, say of size N (who are all married), are in a room. For any given N, I would like to know the probability of at least two people in the room sharing the same birth date (...
- 206
3
votes
1
answer
280
views
How to calculate this dependent probability (marbles without replacement)?
I present the question in two steps:
First:
Let there be 100 bags. A person puts 5 marbles into 5 separate, randomly selected, bags. You are now to collect the contents of the bags, one by one. If you ...
- 135
14
votes
7
answers
7k
views
What is the probability of 4 person in group of 18 can have same birth month?
This is not a class assignment.
It so happened that 4 team members in my group of 18 happened to share same birth month. Lets say June. . What are the chances that this could happen. I'm trying to ...
- 8,043
4
votes
1
answer
2k
views
Calculating the probability of duplication in a random number sample
If I sample 23 random numbers from 1-365, how could I calculate the probability of there being a duplicate?
Context to this question: I was looking into the birthday paradox and I wanted to explore ...
- 43
1
vote
1
answer
261
views
Proper length of random nonce for hash calculation (blockchain)?
I have a string s and I need to calculate a nonce such that when appending the nonce to the string, the generated hash starts with a given sequence. The hash has 256 bits, so the number of ...
- 11
1
vote
1
answer
144
views
Acronyms duplicates (a generalisation of the birthday problem)
I brought more precision into the way I ask this question to make it investigatable:
Assume that everyone has a First name, a Family name, a Street name and a Suburb name. If you make a four-letter ...
- 11
6
votes
2
answers
9k
views
Probability that any two people have the same birthday?
In Blitzstein's Introduction to Probability, it is stated that the probability that any two people have the same birthday is 1/365. However, isn't this the conditional probability that the second ...
- 269
1
vote
0
answers
61
views
Birthday problem extension to unequal probabilities and multiple collisions
Let $p_1, ... ,p_k$ denote the probabilities of drawing bin $1, .. ,k$, where $\sum_{i = 1}^{k} p_i= 1$. My question is if we draw $n$ times, how can I show that the probability of no bin being drawn $...
- 11
1
vote
1
answer
192
views
Variation on the Birthday Problem
You ask an audience one by one for their birthdays. How many people do you need to ask on average until you get your first overlap?
This sounded to me quite similar to a geometric distribution in ...
- 571
2
votes
3
answers
11k
views
Calculating the probability of a 6 digit phone number with no repeats
I have a stats problem I cannot solve, I have the answer and I have attempted the question. I just need to know where I am going off track. Any assistance would be highly appreciated.
Q: What is the ...
- 131
1
vote
1
answer
1k
views
Find the probability that in a group of 23 people, exactly 3 people have birthdays on the same day [duplicate]
My approach was as follows, select 3 people from 23 and then assign any one of the 365 days, then assign the remaining 20 people any of the 364 days and divide it by the total possibilities, which ...
- 560
4
votes
2
answers
4k
views
Birthday paradox: How to estimate the probability of two or more people in a group of 30 sharing a birthday?
I might be overthinking this. I generated the output in R and 5 of my 10 samples were successful, so that's 50%. Given that, if I am to estimate the probability of two or more people in a group of 30 ...
- 41
7
votes
2
answers
275
views
How many Americans, randomly chosen, are needed to have a 50% chance two live in the same or adjacent states?
Background
I'm studying common coincidences and "near" coincidences that nevertheless (unduly) impress the average person. The below question is an extension of the famous Birthday problem, which ...
- 762
5
votes
3
answers
3k
views
Birthday Problem: How am I wrong? [duplicate]
Before reading the Wikipedia article, my idea to calculate the probability was as follows:
$1-\left(\frac{364}{365}\right)^{_nC_{2}}$
Basically, I thought to compare all combinations of pairs ($_nC_{...
- 153
10
votes
2
answers
771
views
Reverse birthday problem with multiple collisions
Assume you had an alien year with an unknown length N. If you have a random sample of said aliens and some of them share birthdays, can you use this data to estimate the length of the year?
For ...
- 101
11
votes
1
answer
772
views
A reverse birthday problem: no pair out of 1 million aliens shares a birthday; what is their year length?
Assume a planet with a very very long year of $N$ days. There are 1 million aliens at a party in a room, and no one at all shares a birthday. What can be inferred about the size of $N$?
(This more ...
- 565
0
votes
2
answers
223
views
Is this a reverse Birthday Problem problem? [duplicate]
I have a machine that generates 16 character long sentences made up of (I think kinda) random letters. I can get it to spit out up to 1 million such sentences before I loose the ability to store them (...
- 565
1
vote
1
answer
170
views
Sampling pairs without replacement from two urns with overlapping populations
I have been trying to derive the coefficient of inbreeding lately, but I am at a loss. If I understand correctly it measures the probability of an allele "collision" i.e. getting the same allele from ...
- 240
2
votes
1
answer
112
views
Efficient random generation for generalized birthday paradox problem?
In generalized birthday paradox problem
The probability of getting $k$ unique values from $[0, n)$ when
choosing $m$ times is given by:
$$P(V = k) = \binom{n}{k}\displaystyle\sum_{i=0}^k (-1)...
Tim♦
- 135k
5
votes
1
answer
140
views
number of different events in a random sequence
I'm confronted with a probability problem that may have already been solved.
I'm considering random sequences of m events.
The number of possible events is n, and each type of event has the same ...
2
votes
1
answer
2k
views
Sample space and outcome of birthday problem
Suppose, calculating the probability of having at least two peoples same birthday from 25 people. What is the sample space and outcome of the experiment?
As far as I pondered, S = 365^25 and outcome ...
- 29
4
votes
3
answers
2k
views
Birthday problem independent events?
The Wikipedia article about the birthday problem explain how to calculate the probability of birthday collision. They're simply telling in the process that the events are independent :
When events ...
- 143
2
votes
1
answer
239
views
Probability of last 3 digits matching in 9 digit student ID
Here is the scenario:
There are a number of students (n), each with a random 9-digit integer student ID number (including zeros). At what n-value would there be a 0.5 probability at least two ...
4
votes
1
answer
697
views
Birthday Problem: Difference between Canonical Solution and Approximation
A couple weeks back, I was seeing if I could solve the basic formulation of the Birthday Problem (i.e. assuming 365 equally likely birthdays, what's the probability that, given a room of ${n}$ people, ...
2
votes
1
answer
226
views
How many identical pairs in a random draw?
I have an infinite stream of good random numbers available to me that range 0 - 255. I draw them in pairs. In how many pairs will both numbers be equal?
I think that this is a form of Birthday ...
- 565
2
votes
1
answer
611
views
What's the expected number of distinct values within a binomial distribution sample?
Given $X$ has a binomial distribution $B(n,p)$. Now I take $k$ samples from $X$. What's the expected value of how many distinct values I sampled?
My rather futile approach was: Given after $k$ draws, ...
- 21
4
votes
1
answer
323
views
Birthday Paradox: does it count if people are born in the same year?
Does the birthday problem change if we only take people from the same year (e.g. a classroom)?
Intuitively I think it does, because you have more probabilities to have two people born in different ...
- 41
0
votes
2
answers
203
views
Just curious of the odds of this happening
Was having lunch with a lover on the boardwalk and he pulled a random couple off of the boardwalk to have lunch with us. As we were talking, we discovered that both men had the same birthday, and the ...
4
votes
3
answers
583
views
Poker and the Birthday Problem
The number of possible poker hands drawn from a standard 5-card deck is ${52 \choose 5}$. This is sampling without replacement where order does not matter, e.g., ...
- 1,051
1
vote
0
answers
182
views
Birthday paradox, two generations, different continents [closed]
I have been reading about the birthday paradox & was trying to take it further & apply it to an example from my own life:-
I am a Brit married to an American.
My British sister-in-law shares ...
7
votes
2
answers
954
views
Birthday "Paradox" -- with a different perspective
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 ...
- 422
35
votes
7
answers
104k
views
Birthday paradox with a (huge) twist: Probability of sharing exact same date of birth with partner?
I share the same birthdate as my boyfriend, same date but also same year, our births are seperated by merely 5 hours or so.
I know that the chances of meeting someone who was born on the same date ...
- 517
5
votes
6
answers
21k
views
What is the probability that a person will die on their birthday?
I am curious about what the probability is that a person will die on their birthday?
I am sure there are a number of ways to approach this, plus I have heard that actual numbers point to a higher ...
- 159
12
votes
1
answer
2k
views
Expected number of duplicates (triplicates etc) when drawing with replacement
I have the following problem:
I have 100 unique items (n), and I'm selecting 43 (m) of them one at a time (with replacement).
I need to solve for the expected number of uniques (only selected once, ...
- 123
2
votes
1
answer
644
views
Birthday problem, but matching couples instead of individuals
Suppose n couples are invited to a party. What is the probability that there are at least
two husband–wife pairs such that the husbands have the same birthdays and so do their
wives?
2
votes
2
answers
158
views
Calculating the probability of the Nth sample in the birthday problem w/o knowing the previous samples
If we draw two random variates from a discrete uniform distribution $[1, D]$, the probability that the samples are distinct is $(D-1)/D$. Explanations of the birthday problem state that if we sample a ...
- 123
3
votes
2
answers
514
views
Probability of Unique Minimum (Discrete)
This is a discrete problem concerning integers.
If there are $n$ independent random variables $X_1,...,X_n$ that each take on a value from $\{1,...,x\}$ uniformly at random ($x$ distinct values), ...
- 133
4
votes
1
answer
888
views
The Birthday Problem, revisited...?
I'm currently facing a problem I have been stuck in for almost half a day and I really can't keep this because I have a lot of work to do! It obviously has to do with the birthday problem.
The ...
- 3,787
14
votes
1
answer
2k
views
What is the real answer to the Birthday question?
"How large must a class be to make the probability of finding two people with the same birthday at least 50%?"
I have 360 friends on facebook, and, as expected, the distribution of their birthdays is ...
- 859
5
votes
1
answer
446
views
Statistical equivalence in the birthday paradox
I was reading a Wikipedia article on the birthday paradox and stumbled upon the following statement:
...the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen ...
- 153
33
votes
3
answers
12k
views
Extending the birthday paradox to more than 2 people
In the traditional Birthday Paradox the question is "what are the chances that two or more people in a group of $n$ people share a birthday". I'm stuck on a problem which is an extension of this.
...
- 331