Probability of birthdays on every day

[duzza275]

Please may someone help me with this and if you have an answer please may you show all the steps that you took. This is not a prep question but I was thinking about it and wondering what the answer was but my statistics skills are not good enough for this yet. :)

If I have a randomly selected group of 430 people. What is the probability that there is 1 birthday on ever single day in the year? (Assume that it is a 365 day year)

Thanks

 

[gsal]

Good luck...I guess you are asking for an answer from the purely mathematical point of view assuming a uniform distribution of births throughout the year?

I am wondering because that's not what REALLY happens. Weather and holidays affect love-making; last I heard, new year's is a 'lucky' day and so, we have a lot of September people.

Just look at the animal kingdom; ok, they don't have holidays, but look at how the times when, basically, the entire group gives birth within a matter of days or weeks ruled by migratory patterns, availability of food, weather conditions, etc.

Anyway, just a thought.

 

[duzza275]

Yeh I am looking for an answer with a mathematical point of view that assumes that births are evenly distributed throughout the year.

 

[awkward]

Please may someone help me with this and if you have an answer please may you show all the steps that you took. This is not a prep question but I was thinking about it and wondering what the answer was but my statistics skills are not good enough for this yet. :)

If I have a randomly selected group of 430 people. What is the probability that there is 1 birthday on ever single day in the year? (Assume that it is a 365 day year)

Thanks

This is the "Coupon Collector's Problem". See my reply to this post

https://www.physicsforums.com/showthread.php?t=523620

for a formula for the probability.

 

[CellCoree]

for your question! This is a great example of using probability to analyze a real-world situation. To solve this problem, we need to use the concept of independent events.

First, let's define the event we are interested in: having 1 birthday on every single day in a 365-day year. This means that each person in the group has a unique birthday, and no two people share the same birthday.

Next, we need to calculate the total number of possible outcomes for this event. Since there are 365 days in a year, and we have 430 people, the total number of possible outcomes is 365^430. This is a very large number, but it represents all the possible combinations of birthdays that could occur in this group.

Now, let's look at the favorable outcomes, or the outcomes that meet our criteria of having 1 birthday on every day. To calculate this, we can use the formula for combinations, nCr, which represents the number of ways to choose r objects from a set of n objects without replacement. In this case, n=365 and r=430, so the formula becomes 365C430 = 365! / (430!(365-430)!). This results in a very small number, indicating that the number of ways to have 1 birthday on every day is much smaller than the total number of possible outcomes.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 365C430 / 365^430. This gives us a probability of approximately 0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000