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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Figuring out N = 23 Birthday Problem - Probability
I am incredibly frustrated so please excuse me.
I know I can just run the computations but I am struggling to figure out algebraically how I can figure out that n = 23 whereby it takes a minimum of 23 ...
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Birthday Problem: Justify Why $n$ is Greater Than $\frac{365}{2}$
Problem (skip to part d): Ignoring leap days, the days of the year can be numbered $1$ to $365$. Assume that birthdays
are equally likely to fall on any day of the year. Consider a group of $n$ people,...
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Birthday Problem: Finding a Probability Function of an Event
Problem: Ignoring leap days, the days of the year can be numbered $1$ to $365$. Assume that birthdays
are equally likely to fall on any day of the year. Consider a group of $n$ people, of which
you ...
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What is the probability that three living people in the same family will celebrate their birthdays on exactly the same day.
I celebrate my birthday on the same day as one of my grandchildren. Just wonder how rare it would be for three people in the same family to celebrate their birthdays on the same day.
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Progressive Birthday problem
The Birthday Problem is very interesting to me. The more dates you fill up, the lower the chances a date will be outside what has already been seen.
But I do not seem to understand at all how ...
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probability of 2 person has the same birthday in a class.
problem: there are n persons in a room, what is the probability that no two of them celebrate the same birthday in a year?
Here is my thought process,
The sample space is $|\{(b_1,b_2,\dots,b_n): b_1,...
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Probability of no birthdays for X consecutive days within a group of n people
Consider a group of n people. Assume 365 days in a year and that birthdays are independent and uniformly distributed.
What is the probably that ...
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What is the expectation value of the minimum 'distance' between two random 64-bit numbers out of a set of N?
Assume we have a set of N random integer numbers in the interval [0, 2^64> (or equivalent, consider N randomly chosen corners (vectors) of a 64-dimensional ...
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At least how many residents of the country have the same birthday?
I am trying to solve a pigeonhole question in discrete mathematics.
Let's suppose that a country has 11.000.000 people. At least how many residents of the country have the same birthday?
Take into ...
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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 ...
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Which would be the "direct" formula for the birthday paradox , withouth subtracting to 1?
I stumbled upon the birthday paradox, and I get it.
However, all the explanations I see solve the probability by subtracting to 1 the probability of all people having different birthdays. What I am ...
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Average number of birthdays today
On Facebook, I can see which friends have birthdays today. Sometimes there are 1, sometimes more than 1, and sometimes zero friends. What's the average number of birthdays today? To formalize:
Problem ...
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Find the probability that at least two people out of $k$ people will have the same birthday
The Birthday problem. Find the probability that at least two people out of $(k=5)$ people will have the same birthday.
The usual approach would be to use $$p=1-\frac{P_{365,5}}{365^5}$$
However, I ...
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Probability distribution for birthday paradox
In Wikipedia we read
In an alternative formulation of the birthday problem, one asks the average number of people required to find a pair with the same birthday. If we consider the probability ...
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Random Variable - Birthday Problem
How many people are needed so that the probability that at least two of them were born on the same day of the week is at least 1/2? (Assume that the days of the week are equally likely to be the ...
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