All Questions
Tagged with birthday probability-theory
29
questions
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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 + ...
- 825
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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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2
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116
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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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Birthday problem with indistinguishable clones.
Suppose we have created an army of n clones which are completely identical(except they may have different birthdays). The cloning happened at different times such that all 365(disregarding the 366th ...
- 13
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What is the probability of at least one pair of people who share a birthday and whose mothers share a birthday?
Problem $71$ of Chapter 4 from Introduction to Probability by J. Blitzstein and J. Hwang.
In a group of $90$ kids, what is the approximate probability of there being at least one pair of kids born on ...
- 273
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At least 2 share the same birthday but without doing actual calculations for the probability
I am reading the following problem:
If $20$ people are selected at random, find the probability that at
least $2$ of them have the same birthday. As a follow up, how large a
group is needed to give a ...
- 1,609
4
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1
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Birthday problem with large $n, d$ values
In the Birthday problem, the formulas
$${\displaystyle {\begin{aligned}p(n;d)&={\begin{cases}1-\displaystyle \prod _{k=1}^{n-1}\left(1-{\frac {k}{d}}\right)&n\leq d\\1&n>d\end{cases}}&...
- 1,561
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Birthday Paradoxon
So I saw this interesting problem:
https://en.wikipedia.org/wiki/Birthday_problem
And I am not the best at probability, so my question is why I cant calculate the probability with
P (2 in n same ...
user763336
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1
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400 people are in a room. What is the probability of two random people having the same birthday? [duplicate]
There are 400 people in a room. I pick two people at random. What is the probability that they have the same birthday?
I know that there must be two people in the room who share the same birthday ...
- 111
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4
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820
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There are 3 people in a room.What is the probability atleast 2 of them share same birthday
I want to know how to solve by NAIVE APPROACH, NOT by taking complement. That is, not by calculating the probability that no one shares a birthday and subtracting from 1 to get the answer.
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Birthday paradox with a twist
My questin is a variation on the birthday paradox problem:
The difference being that here we want to know if two people have the same given birthday, not any same birthday. How would I solve this?
- 417
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What is the probability that in a group of n people chosen at random, there are at least two born in the same month of the year?
So I'm working on a probability problem:
In Exercise 19 assume it is equally
likely that a person is born in any given month of the year.
b) What is the probability that in a group of $n$ ...
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3
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1
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Show that $p_{n} \geq 1- \exp{(-n(n-1)/730)}$
On the issue of the birthday paradox,Let $p_{n}$ be the probability that in a class of $n$ at least $2$ have a their birthdays on the same day (exclude $29$ Feb). Use the inequality $1-x \leq e^{-x}$ ...
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Birthday problem: using $^nC_r$.
In birthday problem say total number of people n < 365, then probability of all person having distinct birthday is given by,
$$\frac{\text{total no. of ways of selecting $n$ numbers from $365$ ...
- 539
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Independent Probability | Duplicate numbers
$11$ numbers between $1$ and $40$ are select. What is the probability there are some duplicated integers in those $11$?
I think the answer to this question is very straightforward: $1-P(\text{they ...
user532588