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.

34 questions
202 views

### Reverse birthday problem with multiple collisions

Assume you had an alien year with an unknown length N. If you have a random sample of said aliens and some of them share birthdays, can you use this data to estimate the length of the year? For ...
58 views

### Variation on the Birthday Problem

You ask an audience one by one for their birthdays. How many people do you need to ask on average until you get your first overlap? This sounded to me quite similar to a geometric distribution in ...
16k 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 ...
77 views

### Probability of last 3 digits matching in 9 digit student ID

Here is the scenario: There are a number of students (n), each with a random 9-digit integer student ID number (including zeros). At what n-value would there be a 0.5 probability at least two ...
38 views

### Birthday problem with three people [closed]

Suppose there are three persons: A, B and C (randomly picked from a cohort which has the same birth year). Now three mutually exclusive events can happen: $X$: all of them born on different dates, the ...
107 views

### What's the expected number of distinct values within a binomial distribution sample?

Given $X$ has a binomial distribution $B(n,p)$. Now I take $k$ samples from $X$. What's the expected value of how many distinct values I sampled? My rather futile approach was: Given after $k$ draws, ...
1k views

### Calculating the probability of a 6 digit phone number with no repeats

I have a stats problem I cannot solve, I have the answer and I have attempted the question. I just need to know where I am going off track. Any assistance would be highly appreciated. Q: What is the ...
400 views

### Birthday “Paradox” — with a different perspective

Background: Many people are familiar with the so-called Birthday "Paradox" that, in a room of 23 people, there is a better than 50/50 chance that two of them will share the same birthday. In its more ...
300 views

### Poker and the Birthday Problem

The number of possible poker hands drawn from a standard 5-card deck is ${52 \choose 5}$. This is sampling without replacement where order does not matter, e.g., ...
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, ...
104 views

### Find the probability that in a group of 23 people, exactly 3 people have birthdays on the same day [duplicate]

My approach was as follows, select 3 people from 23 and then assign any one of the 365 days, then assign the remaining 20 people any of the 364 days and divide it by the total possibilities, which ...
315 views

### Probability of Unique Minimum (Discrete)

This is a discrete problem concerning integers. If there are $n$ independent random variables $X_1,...,X_n$ that each take on a value from $\{1,...,x\}$ uniformly at random ($x$ distinct values), ...
78 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 ...
169 views

### How many Americans, randomly chosen, are needed to have a 50% chance two live in the same or adjacent states?

Background I'm studying common coincidences and "near" coincidences that nevertheless (unduly) impress the average person. The below question is an extension of the famous Birthday problem, which ...
542 views

### Sample space and outcome of birthday problem

Suppose, calculating the probability of having at least two peoples same birthday from 25 people. What is the sample space and outcome of the experiment? As far as I pondered, S = 365^25 and outcome ...
165 views

### Birthday paradox, two generations, different continents [closed]

I have been reading about the birthday paradox & was trying to take it further & apply it to an example from my own life:- I am a Brit married to an American. My British sister-in-law shares ...
952 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 ...
2k views

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 ...
400 views

### Statistical equivalence in the birthday paradox

I was reading a Wikipedia article on the birthday paradox and stumbled upon the following statement: ...the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen ...
727 views

### The Birthday Problem, revisited…?

I'm currently facing a problem I have been stuck in for almost half a day and I really can't keep this because I have a lot of work to do! It obviously has to do with the birthday problem. The ...