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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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)...
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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 + ...
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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:
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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;
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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 ...
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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, ...
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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 ...
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$T$ 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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