# Unknown Problem - Need Help

This question is from an article I read online, titled: "Why I Will Never Have a Girlfriend" by Tristan Miller.

The author shows his work, step-by-step throughout most of the article, except during the conclusion, when he makes the following statement:

• "At first glance, a datable population of 18,726 may not seem like such a low number, but consider this: assuming I were to go on a blind date with a new girl about my age every week, I would have to date for 3,493 weeks before I found 1 of the 18,726."

He does not explain how he determined 3,493 is the number required to find 1 of the 18,726. I would really like to know. It seems similar to the Birthday Paradox, but I'm not certain?

Thank you in advance for any help / clue. I would especially appreciate anyone who explained, step-by-step how to figure this out, mathematically.

P.S. Apologies; I am not even certain exactly what type of math problem this even is, or what to call it.

• You forgot to mention that he is considering a sample space of $65\,399\,083$ girls aged between $18$ and $25$. – Christian Blatter Mar 4 '15 at 9:17
• My apologies. This problem honestly threw me through a loop; I can't believe I missed that! My mind was totally focused on this being some kind of combination/permutation problem that I was totally blind to the obvious solution. I thought that the author's conclusion section was a self-contained problem, and not related to the numerous previous statements he made earlier in the paper, thus I didn't realize the relevance. – questionthis Mar 4 '15 at 12:25

If he dates blindly (uniformly at random from all girls his age) once every week, the probability he will meet a dateable girl on any given week is $$p = \frac{18726}{65399083}.$$ The inverse $1/p$ is the expected time in weeks (mean of geometric distribution) till he meets a girl from the dateable set and is the number you want: $$\frac{1}{p} = \frac{65399083}{18726} = 3492.42139.$$