We all have a birthday month, and for that matter a certain day in that month. It is always interesting to see if any one famous, other than you, was born in that month. Just in case you might think you are not famous, look it up. Merriam Webster says ‘famous’ is someone known to many. Many is an indefinite number of people. I definitely don’t know the exact number of people who know me. Therefore an indefinite number of folk know me. That actually fits most of us, if not all.
Be that as it may, my month has folks like Thomas Jefferson, Leonardo DaVinci, William Shakespeare and the current Queen of England. Of course, there are also a lot of recent celebrities. However, today’s celebrities are tomorrow’s reality stars or something a little less glamorous.
The real question might be what the statisticians call the Birthday Paradox. That is how many people, say in a room of strangers, have the same birthday as yours. That is a puzzle.
The amazing thing is how little a number it actually takes. It really isn’t hard to logically figure the probability out. The straight math is, like a lot of math, relatively simple but a bit like grinding a big block of wood into a pile of wood dust. It takes time.
Take your birthday, for instance, it is one day out of the 365 days of a normal year. There are 364 days that aren’t yours. When you think about it, the next person you meet has a one out of 365 days chance of their birthday being the same as yours and a 364 out of 365 (364 divided by 365) of not being yours. That is a 99.7 chance it isn’t yours.
To figure out what the probability that anyone in the room would have your birthday seems daunting at this point. However, if you remember that the two events are mutually exclusive, it is yours or it is not yours, then it becomes simpler.
In a two person deal as described above the probability your birthday is yours is certain or one. The chance of their birthday is 99.7 that it isn’t yours. So the chance that it is yours is I minus 99.7 or a 0.03 chance.
Now you can grind the block through the number of people in the room with similar combinatorial math. As you move through the second, third, fourth and so on you will get to 23 and at that point you discover that the chance is slightly better than a coin flip that one of them has the same birthday as yours. If you grind on through to 70 folks, you would find that there is a better than 99.7 chance that someone has your birthday.
Leap year and other things can change the decimal point, Mathematicians use things like binomial coefficient and factorial to make it more elegant. But, the fact is it is a very small number.
