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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\frac{K}{\pi^{2}}$.
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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