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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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'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 ...
josinalvo's user avatar
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2 votes
1 answer
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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)... ...
George Robinson's user avatar
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 + ...
LexLarn's user avatar
  • 825
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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: ...
Equinoccio's user avatar
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; ...
Yuri S VB's user avatar
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 ...
konofoso's user avatar
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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, ...
Julien Maas's user avatar
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 ...
svetysh's user avatar
  • 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 ...
J. Doe's user avatar
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1 vote
2 answers
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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 ...
Dee Kay's user avatar
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0 votes
2 answers
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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 ...
gjlmotea's user avatar
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 ...
Starlight's user avatar
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2 votes
3 answers
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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 ...
Starlight's user avatar
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1 vote
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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 ...
Nigel1's user avatar
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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 ...
Starlight's user avatar
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1 vote
1 answer
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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 \...
user avatar
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 ...
user avatar
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 ...
Malachy_P's user avatar
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 ...
Lawton's user avatar
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0 votes
2 answers
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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 ...
user2051731's user avatar
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 ...
Djalal Ounadjela's user avatar
-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", ...
Heidegger's user avatar
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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 ...
AltercatingCurrent's user avatar
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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 ...
adriaanJ's user avatar
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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=...
jorisperrenet's user avatar
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 ...
ryvantage's user avatar
  • 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 ...
knightdialer's user avatar
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: ...
DTJ's user avatar
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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: ...
DTJ's user avatar
  • 97
0 votes
0 answers
595 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 ...
Ska's user avatar
  • 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 ...
Louis's user avatar
  • 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 ...
nezam jazayeri's user avatar
1 vote
1 answer
773 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 ...
David Rinkes Pastor David's user avatar
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 ...
TwoFluidCarrots's user avatar
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 ...
Ungar Linski's user avatar
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 ...
user107952's user avatar
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0 votes
1 answer
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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 ...
math n00b's user avatar
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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 $\frac{K}{\pi^{2}}$. ...
j13r's user avatar
  • 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.
Violettttt's user avatar
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 ...
Camelot823's user avatar
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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 ...
wxist's user avatar
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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 ...
Ratface's user avatar
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 ...
Jethro Cao's user avatar
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 ...
CJ Dennis's user avatar
  • 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 ...
crypt's user avatar
  • 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 ...
Jimmy Yang's user avatar
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 ...
Homer Jay Simpson's user avatar
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 ...
Kolja's user avatar
  • 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 ...
W. Zhu's user avatar
  • 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 ...
Ernesto Gómez's user avatar

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