There are "n" amount of people in a group. It can be a classrooom, a large lecutre hall, a small crew in a company, etc.
How likely is it that two people will share the same birthday?
But more importantly...
How many people do you need in a group so that the probability that two people will have the same birthday is 50%?
To begin to answer this problem, I followed the guiding questions provided:
Because I had no idea where to even begin with this problem, I decided to multiply up all of the probability percentages beginning at 364/365, to see how many fractions I had to multiply to get a final result of 50%.
After spending a ridiculous amount of time on this method, I got the sam answers that many of my classmates got- 23 people. But, I knew there had to be a "short cut". Mr. Tejera pushed me to think about how to "cancel out factorials" and after discussing with my peers, we came to this final answer:
365! / 365n (365-n)
In this, we use factorials to more easily insert numbers for (n) to learn what will give us close to 50%.
When Mr. Tejera walked our class through his answer, we had similar answers. I enjoyed the process of struggling through solving this problem in a really prolonged way, becuase when I finally compiled it all into a formula, it was really rewarding. I don't have a lot of experience working with factorials yet, so it was also nice to be a little challenged with this problem- above that, it was fun to find out that only 23 people are needed in a group for the percentage of two sharing a birthday to be 50%. That's pretty surprising.
How likely is it that two people will share the same birthday?
But more importantly...
How many people do you need in a group so that the probability that two people will have the same birthday is 50%?
To begin to answer this problem, I followed the guiding questions provided:
- How many birthdates are there in a regular year (not including leap year)?
- In a regular year, there are 365 possible birthdates.
- If my birthday is April 19th, and I meet a new person without the same birthday, how many other days of the year can they possibly have their birthday?
- A new person without my exact same birthday must have their birthday on 364 of the other days in the year.
- What about a third person? On what other possible days can this third person have their birthday so that it is not on the same as the me or the second person?
- Following the pattern, the third person can have their birthday on 363 of the 365 days in the year.
Because I had no idea where to even begin with this problem, I decided to multiply up all of the probability percentages beginning at 364/365, to see how many fractions I had to multiply to get a final result of 50%.
After spending a ridiculous amount of time on this method, I got the sam answers that many of my classmates got- 23 people. But, I knew there had to be a "short cut". Mr. Tejera pushed me to think about how to "cancel out factorials" and after discussing with my peers, we came to this final answer:
365! / 365n (365-n)
In this, we use factorials to more easily insert numbers for (n) to learn what will give us close to 50%.
When Mr. Tejera walked our class through his answer, we had similar answers. I enjoyed the process of struggling through solving this problem in a really prolonged way, becuase when I finally compiled it all into a formula, it was really rewarding. I don't have a lot of experience working with factorials yet, so it was also nice to be a little challenged with this problem- above that, it was fun to find out that only 23 people are needed in a group for the percentage of two sharing a birthday to be 50%. That's pretty surprising.