All Questions
Tagged with birthday combinatorics
94
questions
2
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2
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96
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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 ...
- 21
0
votes
1
answer
65
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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 ...
- 1,834
2
votes
3
answers
62
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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 ...
- 1,834
1
vote
2
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158
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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 ...
- 1,834
1
vote
1
answer
97
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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 \...
user1289955
1
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1
answer
96
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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 ...
user1289970
1
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0
answers
91
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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 ...
- 24
-1
votes
3
answers
72
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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", ...
- 3,482
1
vote
1
answer
195
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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 ...
1
vote
2
answers
114
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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 ...
- 1,467
0
votes
1
answer
43
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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 ...
- 103
-1
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2
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69
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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 ...
1
vote
2
answers
64
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Approximating an inequality with extremely large numbers
I am trying to work out the number of 12 item sequences needed to have a greater than 50% probability that two of these are the same. So far, I have got
$$
1 - \frac{2048^{12}!}{\left(2048^{12}-n\...
- 241
4
votes
3
answers
620
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Probability of Adjacent Birthdays
Recall the birthday problem, where only 23 people are required for a >50% chance that at least two share the same birthday.
What is the new probability if we want at least two people out of twenty-...
- 1,437
2
votes
1
answer
114
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Probability that there exist at least one day without any Birthday
Probability that a given day do not have any birthday among N people is: (364/365)^N
However, what will be the probability that there exist at least one day in a year that have no birthday?
This ...
- 123