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.
351
questions
3
votes
3
answers
153
views
'deducing' a bound using the first order taylor series. How to make it more precise?
So, I just saw a ‘proof’ that the generalized birthday problem has a median of C*sqrt(n). Though the probability in question is interesting, this question is more about calculus and maybe asymptotics ...
- 1,376
2
votes
1
answer
52
views
How to modify the birthday formula to account for overlapping sequences?
While calculating the probability that the same sequence of 50 words occurs twice in a file that contains 400 million random words (each word can have 65536 different states, chosen at random)...
...
- 347
1
vote
1
answer
65
views
Probability problem (maybe linked to birthday paradox)
Good evening. I would like to show the following statement :
Let $n>1$, and $E,F$ two subsets of $[\![ 1,n ]\!]$ randomly and independently chosen such that $|E| = |F| = \lfloor\sqrt{ n }\rfloor + ...
- 825
0
votes
0
answers
25
views
Expected number of collsions in hashing
Suppose we use a hash function h to hash n keys into m slots. Assuming simple uniform hashing, what is the expected number of collisions? (CLRS, 3rd edition, problem 11.2-1)
My solution is as follows:
...
2
votes
1
answer
119
views
What is the limit probability an element of $x \in S$ belongs to $f^n(S)$, for $n \to \infty$?
Let $S$ be a finite set of $|S|=n$ elements and $F$ be the set of all functions $f:S\rightarrow S$.
It's easy to demonstrate that the integer sequence $\{c_i\} = |{\rm Im}(f^i)|$:
is non increasing;
...
- 21
2
votes
2
answers
83
views
Modifying the Birthday Problem Paradox for Arbitrary Situations?
We learned about the birthday problem paradox: If people are in a room with randomly distributed birthdays, very few people are needed for at least two people to have the same birthday.
As I ...
- 765
0
votes
0
answers
35
views
Understanding the generalized "Birthday Problem" formula [duplicate]
While practicing frequently asked probability questions during interviews, I came across the classical "Birthday problem". While I understand some of the reasoning explained on wikipedia, ...
- 39
2
votes
2
answers
96
views
Variation of Birthday problem with n people and exactly t pairs sharing the same birthday
The problem statement is simple: Let there be a group of n people. What is the probability that exactly t pairs will share the same birthday?
All my attempts to solve this problem came down to the ...
- 21
3
votes
1
answer
149
views
$T$ Pokemon trainers catch a Pokemon every day. How many days does it take until two trainers own Pokemons of the same species?
$T$ Pokemon trainers catch $1$ out of $P$ different species of Pokemons every day.
Every species has the same chance to be caught.
One species can be caught by one trainer multiple times.
In mean ...
- 77
1
vote
2
answers
150
views
What is the probability of someone being born both on a Good Friday that is also Friday the 13th
I was born on April the 13th 1990. The day was also Good Friday. I'm wanting to know what the probability/chances of being born on a Good Friday that is also a Black Friday is/are to have an ...
- 51
0
votes
2
answers
243
views
The Facebook Birthday Problem（Birthday Problem Variation） [closed]
The Facebook Birthday Problem:
This problem stems from the classic Birthday Paradox.
It says:
How many friends do you need for the probability of having at least one friend with a birthday each day ...
- 19
0
votes
1
answer
65
views
Order matters or not in birthday probability
In this answer, the choices for the distinct birthdays of single people are counted as if order matters:
$$363\times 362...$$
But the choices for the birthdays of the two pairs(four people) that have ...
- 1,834
2
votes
3
answers
62
views
Verification of answer in a birthday problem
In the answer here, should the number of ways to pick the groups of triples, pairs and singlets from the 20 people be:
$$\frac{20!}{\color{#C00}{3!^2}\,\color{#090}{2!^4}\,\color{#E90}{6!}}$$
since if ...
- 1,834
1
vote
2
answers
71
views
Birthday problem: how to show the scaling with $1/N^2$?
Suppose there is a sequence of$N$ numbers $x_1, x_2, x_3, ... x_N$.
There are then gaps $|x_i - x_j|$, and the minimum gap:
$\delta (N) = \text{min}_{i \ne j \le N} \{ | x_i -x_j | \}$.
Let the mean ...
- 655
1
vote
2
answers
158
views
Birthday problem with shared birthdays among males and female students
There are $m$ male and $f$ female students in a class (where $m$ and $f$ are each less than 365) What is the probability that a male student shares a birthday with a female student?
I have attempted ...
- 1,834
1
vote
1
answer
97
views
Why isn't adding the ways to achieve every mutually exclusive outcome giving me the denominator in the birthday problem for four people?
Why isn't adding the ways to achieve every mutually exclusive outcome giving me the denominator in the birthday problem for four people?
$$\binom{4}{2} \cdot 365 \cdot 364 +\binom{4}{3} \cdot 365 \...
user1289955
1
vote
1
answer
96
views
Where in the original statement of the birthday problem is the order people of assign matter in the numerator of the probability?
In $\dfrac{365 \choose \#people}{365^{\#people}}$
this counts no repeats for the probability of none assuming Jan, Feb, March is the same thing as Feb, March Jan.
If
We interpret the question as ...
user1289970
1
vote
0
answers
91
views
Birthday Paradox Variant: Probability of getting X days with only one birthday [duplicate]
I don't know whether this question has been asked or not, or if it's on the Wikipedia, and apologies if so but I wanted to know:
Given a group of n people, what is the probability of X people having ...
- 24
2
votes
1
answer
49
views
Is there a closed-form inverse of the Birthday Problem equation over the interval $1 < k < n + 1$?
The Birthday Problem deals with the probability that, in a set of $k$ randomly-chosen people, at least two will share a birthday. It can be generalized to similar questions of a match with any pair ...
- 1,861
0
votes
2
answers
74
views
Expected number of days which are birthdays for k people - confused by linearity intuition
I understand this has been asked before but I still cannot understand the intuition behind it. A lot of the answers I've seen seem to just state that it's due to linearity of expectation and that it ...
- 37
5
votes
2
answers
146
views
Probability that among $n$ random people, at least two have coinciding or successive birthdays
I found the following riddle:
What is the probability that among $n$ people chosen randomly, at least two of them have their birthdays with at most one day difference.
Note: December 31 and January ...
- 1,172
-1
votes
3
answers
72
views
Doubts about the Birthday Problem [closed]
I was thinking about the birthday problem, in a slight different version. In the birthday problem, no date is chosen in advance. The variant I'm thinking of is then "same birthday as you", ...
- 3,482
2
votes
2
answers
137
views
How do the graphs of the "Birthday Probability" functions work?
The question was to find the probabilities that:
At least two people have the same birthday
Only two people have the same birthday
Nobody has same birthdays
in a room of n people.
I did find the ...
0
votes
0
answers
62
views
What is the probability that $n$ persons have birthdays all within one half year?
I'm wondering what the probability is that $n$ persons have birthdays all within 1/2 year.
For instance, two persons always have birthdays within 1/2 year, as the maximal distance between two days is ...
- 629
0
votes
1
answer
77
views
Chance that a group of $n$ people collectively have a missing birthday.
Suppose there is a city with $n$ residents, what is the probability that there is some day in the year at which none of them have their birthday?
In other words, suppose we divide $n$ balls into $k=...
- 2,305
0
votes
1
answer
27
views
Ongoing "cost" of generating a number at random until it doesn't collide
There's a company which gives each customer a unique numeric ID (between 10000000-99990000). Every time a new customer record is created, the algorithm generates a random number and checks if the ID ...
- 131
-2
votes
1
answer
75
views
Why can't I use a direct approach in the birthday problem?
In a variation of the birthday problem, we are trying to find the probability that another student in the class shares our birthday. We can use the complement rule to find the probability that a ...
1
vote
1
answer
90
views
Need to explain the result of the birthday problem?
I am working with a question of birthday problem, and here is the case I have to solve:
...
- 97
0
votes
1
answer
55
views
Clarify the solution for the birthday problem with more than 2 people in a group of n people
I am a newbie with the Statistic and Probability, and I was encountered with the birthday problem. And here is is the question I have to answer:
...
- 97
0
votes
0
answers
591
views
Estimate of peoples sharing the same first name, last name and date of birth over a population
I am aware of the birthday paradox (more than 50% likeliness of two people sharing the same day of birth). My question is somehow related to this, but with more variables (and unknowns).
Given a total ...
- 1
0
votes
0
answers
164
views
Formula for the probability of two people with the same name in a group.
I'm looking to figure out a formula that can help me calculate the probability that two people in a group share the same full name. Specifically, my question is: In a group of $X$ people (ranging ...
- 1
5
votes
1
answer
337
views
Unknown distribution for birthday problem
Coming from Blitzstein's book:
In the birthday problem, we assumed that all 365 days of the year are
equally likely (and excluded February 29). In reality, some days are
slightly more likely as ...
- 449
1
vote
1
answer
768
views
Family Members Birthday Dates all different, but our birthdays will fall on same day, even Leap Years. There is a total of 9 in this Birthday Club. .
I can compile a list if needed and post, but I noticed this over 50 years ago, My Father, My Brother and Myself our Birthdays fall on the same day of the week every year. Even Leap years, that does ...
1
vote
1
answer
195
views
Birthday Problem: Confusion between PMF and CDF -
The question:
(Introduction to Probability, Blitzstein and Nwang, p.128)
People are arriving at a party one at a time. While waiting for more
people to arrive they entertain themselves by comparing ...
2
votes
0
answers
78
views
How many people must be in a room until it is at least a $50\%$ chance that two will have the same amount of change?
Book problem: If the amount of change in a pocket is assumed to be uniformly distributed from $0$ to $99$ cents, how many people must be in a room until it is at least a $50\%$ chance that two will ...
- 757
0
votes
0
answers
45
views
The Birthday paradox with variable-likelihood birthdays. [duplicate]
I know that the Birthday Paradox is the fact that in a room of 23 people, the chances are more than 50 percent that at least two people share a birthday. However, this is under the assumption that all ...
- 21.4k
0
votes
1
answer
74
views
Birthday Problem Confusion Using the Counting Rule
I am stumped by the below confusion:
Question: How many people do we need in a class to make the probability that (at least) two people have the same birthday more than 1/2? (For simplicity, assume ...
0
votes
0
answers
50
views
Number of date collisions in birthday problem
If I generate uniform random integers from 1 to K and count how many unique numbers I get $n_\mathrm{unique}$, I empirically obtain:
the mean is: $\frac{2K}{\pi}$
the variance is $\frac{K}{\pi^{2}}$.
...
- 365
-3
votes
1
answer
65
views
How can I prove that the probability that exactly 2 people share the same birthday is more likely than everyone has a different day out of 20 people? [closed]
I will be thankful if you can help me and show how to solve this.
1
vote
2
answers
114
views
Miscalculating Probability of At Least $2$ People Having The Same Birthday
Regarding the problem: choosing 23 people randomly, show that there is greater than a $50$ percent chance that at least two of them will have the same birthday. What is the error in the way I'm trying ...
- 1,467
0
votes
0
answers
49
views
Classmate birthday Probability [duplicate]
I dealt with one issue, namely:
Consider $k$ independent realizations of a random variable uniformly distributed over a set of $n$ values.
1 What must $k$ be for the probability that the given outcome ...
- 481
0
votes
1
answer
74
views
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 ...
- 1
0
votes
1
answer
43
views
Help with deriving solution for multiple birthday problem
I've been thinking about one version of the more general birthday problem, namely for the case of k $\ge$ 3. I found this document explaining the solution through a combinatorial method, but I'm ...
- 103
1
vote
1
answer
102
views
How to work out the probability of two random sequences sharing a certain number of matches?
Pick two sequences of numbers, $S_1$ and $S_2$. $S_1$ is $n_1$ picks from $1$ to $k$, $S_2$ is $n_2$ picks from $1$ to $k$. There could be duplicates within each sequence, for instance $S_1$ might ...
- 664
0
votes
1
answer
61
views
Collisions in a Sample [closed]
Based on birthday paradox;
Let $d$ be the set of elements randomly chosen from a set of $n$ distinct elements then
a) What is expected number of unique elements in $d$ (remaining will be repetition of ...
- 143
1
vote
0
answers
207
views
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 ...
- 454
0
votes
2
answers
116
views
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 ...
5
votes
1
answer
200
views
Birthday paradox - variance, parallelisation, simple proofs?
I am looking for an elementary proof of the fact that expected time for finding a colision with $n$ bins is $\sqrt{\frac{\pi n}{2}} + O(1)$. The proof that I knows relies on the asymptotic expansion ...
- 2,889
4
votes
1
answer
115
views
What is the probability of sharing a birthday if a year has an infinite number of days?
Here is the problem:
Suppose that there are $k$ people. Each of them independently picks a uniformly random number from the set $\{1, 2,...,n\}$. We say that a collision happens if there exist two ...
- 1,345
-1
votes
2
answers
69
views
How many days with birthdays are in a classroom?
Assumption:
I am a teacher of a classroom with n students. And every time there is one or more birthdays in a day, I will buy only a cake.
Question:
How many cakes do I have to buy on average every ...
