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Questions tagged [birthday-paradox]

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.

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30
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3answers
9k views

Extending the birthday paradox to more than 2 people

In the traditional Birthday Paradox the question is "what are the chances that two or more people in a group of $n$ people share a birthday". I'm stuck on a problem which is an extension of this. ...
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1answer
1k views

What is the real answer to the Birthday question?

"How large must a class be to make the probability of finding two people with the same birthday at least 50%?" I have 360 friends on facebook, and, as expected, the distribution of their birthdays is ...
11
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1answer
480 views

A reverse birthday problem: no pair out of 1 million aliens shares a birthday; what is their year length?

Assume a planet with a very very long year of $N$ days. There are 1 million aliens at a party in a room, and no one at all shares a birthday. What can be inferred about the size of $N$? (This more ...
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7answers
72k views

Birthday paradox with a (huge) twist: Probability of sharing exact same date of birth with partner?

I share the same birthdate as my boyfriend, same date but also same year, our births are seperated by merely 5 hours or so. I know that the chances of meeting someone who was born on the same date ...
3
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1answer
440 views

Birthday Problem: Difference between Canonical Solution and Approximation

A couple weeks back, I was seeing if I could solve the basic formulation of the Birthday Problem (i.e. assuming 365 equally likely birthdays, what's the probability that, given a room of ${n}$ people, ...
10
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1answer
1k views

Expected number of duplicates (triplicates etc) when drawing with replacement

I have the following problem: I have 100 unique items (n), and I'm selecting 43 (m) of them one at a time (with replacement). I need to solve for the expected number of uniques (only selected once, ...
5
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6answers
17k views

What is the probability that a person will die on their birthday?

I am curious about what the probability is that a person will die on their birthday? I am sure there are a number of ways to approach this, plus I have heard that actual numbers point to a higher ...
5
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3answers
2k views

Birthday Problem: How am I wrong? [duplicate]

Before reading the Wikipedia article, my idea to calculate the probability was as follows: $1-\left(\frac{364}{365}\right)^{_nC_{2}}$ Basically, I thought to compare all combinations of pairs ($_nC_{...
5
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1answer
80 views

number of different events in a random sequence

I'm confronted with a probability problem that may have already been solved. I'm considering random sequences of m events. The number of possible events is n, and each type of event has the same ...
4
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3answers
1k views

Birthday problem independent events?

The Wikipedia article about the birthday problem explain how to calculate the probability of birthday collision. They're simply telling in the process that the events are independent : When events ...
4
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2answers
1k views

Birthday paradox: How to estimate the probability of two or more people in a group of 30 sharing a birthday?

I might be overthinking this. I generated the output in R and 5 of my 10 samples were successful, so that's 50%. Given that, if I am to estimate the probability of two or more people in a group of 30 ...
0
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2answers
85 views

Just curious of the odds of this happening

Was having lunch with a lover on the boardwalk and he pulled a random couple off of the boardwalk to have lunch with us. As we were talking, we discovered that both men had the same birthday, and the ...
0
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2answers
162 views

Is this a reverse Birthday Problem problem? [duplicate]

I have a machine that generates 16 character long sentences made up of (I think kinda) random letters. I can get it to spit out up to 1 million such sentences before I loose the ability to store them (...