I am not a statistics expert but was interested in the validity of the reasoning below.
Somebody argued that many people had the letter 'J' in their initials. Can someone comment on the validity of the following approach and how it could be improved, notably what probability distribution would a list of firs tnames sorted by popularity follows?
According to wikipedia the most common first names for males in the US according to the 1990 census are, in that order:
'James','John','Robert','Michael','William','David','Richard','Charles','Joseph', and 'Thomas'
Let's use an approximate probability distribution (any better way?) that gives the probabilities to these names according to their order i (starting at 0) following:
P(name_i) = 0.15 / (i + 2)
This is a probability distribution for at least 1000 names (sums to 1), and starts like this:
0.0749, 0.0499, 0.0374, 0.0299, 0.0249, ...
meaning that someone has 7.49% chances of being called James. The sum of the probabilities of having a name starting with J from these list is 14% (P(James)+P(John)+P(Joseph)), lets call it Pj. Of course Pj is in fact higher because more names than these 8 in the list of 1000 may start with J.
Now let's assume a child is given three first names, the probability that at least of them starts with J given pj is 36%!! (from (1-(1-pj)^3)). So every time you meet a new person, you have one third chances to see him having a J on his business card. Let's call this probability pIj, probability of at least one initial starting with a J.
However, when you say overwhelming majority, let's assume that you mean 8 out of 10. The probability that out of 10 people you meet in a row 8 have a name starting with a J is, using binomial distribution, only 0.5% I'm afraid, by comb(10,8)pIj^8(1-pIj)^2 .
However, if you settle with 5 our of 10, your chances rise to 16%.
FYI the original question and post can be found here.