I give blood. I got a call from the local blood bank that there is another woman with the exact same birthdate, including year, same first name, and same blood type with a different last name, so she needed to know if that was also me. It is not.
So, now I am curious - what are the odds of that? I live in the Chicago area. For the 2000 census, there were 8,376,601 people in this area. But then I was able to find it broken down - so there are 57,930 women born the same year I was in my area. I looked on the social security web site, and the odds that a woman would have my first name if born in the 1970s is 7.5%. I know my blood type is usually found in 6% of the population from the pamphlets they give you to read when you give blood.
There are two figures I am having trouble identifying. What are the odds that someone would share my exact same birthdate, year and all, and what percent of people actually give blood? I guess I already have it narrowed down to the year, so I just need to know the odds that someone would have the same birthday. Is it fair to say it is 1 out of 365? My birthday is January 10th. I am not sure if that is a time of year with more births than usual or not. I will ignore the fact that I give blood with two different organizations and the one who called is the less popular of the two.
It doesn’t matter for anything but curiosity sake. But does anyone care to help?
I don’t know what fraction of people give blood, but (assuming all birthdays are equally probable) the odds of someone sharing your birthday are 1/365 or 0.00274.
So if everyone gave blood, the odds of someone else having the same birthday, name and blood type as you is (0.0006916)(0.00274)(0.075)*(0.06) = 0.0000000853 (8.53E-8). Multiply this by the fraction of people who give blood to get a rough estimate of the probability of this occuring…
Now the odds of this happening to anybody, and not just you, are much higher.
I didn’t phrase my first sentence well – I wanted it to say that I think it is a pretty good approximation to assume that all birthdays are equally probable, and thus I agree with your 1/365 figure. It currently reads like I didn’t actually read the OP, which I did. For once.
Well, I just found a website that says it is estimated that 8 million people give blood every year, or 5% of the population. It said white men between 30 and 50 are the highest percentage. So do we assume 5%, or something higher? I am in the more popular race and age brackets, but not the more popular gender bracket.
I know what you mean about happening to anyone versus just me. I remember that one of the ice breakers we did in a physics class in college. The TA bet us that there would be two people in the room with the same birthday. There were 26 people in our class, and he was right - there was a set. He then explained how it is likely to have two people share a birthday if you have more than 17 people in your sample.