Posted on Wed 12/28/05 in Technical Interleude
I found out about a year ago that I have an older half-sister. While I’ll probably fill in the blanks about this story at a later time, this post will touch on one interesting aspect…
My half-sister, who was adopted just after her birth, was given the same name by her foster parents as one of my two younger sisters. I find that pretty amazing. But, how amazing, exactly?
Jim, my newly acquired brother-in-law from my recently discovered sister, proposed the question this weekend while he was visiting us: What are the chances that the two of them had the same name? Is it coincidence?
We considered for a bit the formula which would determine the chances of this occurring, but we decided to consider it at a later time. Yesterday, I asked the question on answers.google.com.
You can view the question and the comments posted by clicking the link above. The Google Answers project allows people to post questions for “researches” to answer for a set price. In my case, I offered $15 for the answer; however, since the answer was determined to my satisfaction by unpaid non-researchers and me, I changed the amount to the minimum $2.
The following is my determination:
P(x) is the probability of each child mutually exclusively being given a specific name, based on the popularity of the name for the year she was born and on the total number of births for that year. The data was taken from www.ssa.gov.
P(Sister1) = 0.8597% = .008597
P(Sister2) = 1.8762% = .018762
I then see the P(Sister) and P(Sister2) BOTH happening is:
P(Sister1) * P(Sister2) = .008597 * .018762 = 0.000161296914 ~ a 1/6200 chance.
According to http://funny2.com/odds.htm, that’s about the same odds as injuring yourself while shaving.
And according to http://www.nsc.org/lrs/statinfo/odds.htm, that’s roughly as probable as one dying from a “fall from out of or through building or structure.”
That’s pretty unlikely if you ask me. Is this unlikely enough to be considered more than just coincidence?
During my initial conversation with Jim, it was our misconception that their relation as sisters was relevant for the scope of this question. Since the names were given independently to each of the girls, the fact that they are sisters, is irrelevant. Whether there is supernatural relevance, outside the scope of this mathematical question, is something entirely different.
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