How are these probabilities being calculated This is an excerpt from the BBC website:

A recent study into speed dating habits concluded that if men and
  women go to an evening and have 22 separate dates, men are keen to see
  about five women again, while women would only choose to see two
  again, on average.
That means that for every offer a woman makes, she has roughly a 50-50
  chance that the man will want to see her again too.
But for every offer a man makes, he only has a one in five chance that
  the desire to meet again is reciprocated.

I have read the story a few times, but I don't see how the probabilities (of a successful date) for men and women are being calculated. Anyone care to shed some light on this?
 A: The question has a lack of clarity in its explanation - that much is beyond doubt. 
Consider the question of 'how many men and how many women are present?'.
We are told there are "22 separate dates". Is that 22 of each sex? Well, I don't think it can be. My understanding of speed dating is that each person spends time with every potential partner*. 
* (speed dating for gays or lesbians might involve some kind of round-robin scheduling in place of the straight cycling around of heterosexual speed dating, I guess. Edit: In fact, I think I've just realized how to set up the tables and everything, even with an odd number.)
Let's assume there are equal numbers of males and females. If there were 3 of each sex, how many dates would there be?
Labelling females with letters (A,B,C) and males with numbers (1,2,3) we get:
A1 A2 A3
B3 B1 B2
C2 C3 C1 
(you can read the columns as rounds, and in this schedule the males are cycling around the tables while the females stay in place)
That's 9 dates from 3 pairs of each sex, 3 pairs in each of three rounds. And indeed, similarly, $n^2$ separate dates for $n$ daters of each sex.
With my keen eye and (to the BBC at least) uncanny ability with arithmetic, I have spotted that 22 isn't a square, so "22 separate dates" doesn't work at all. Since it seems there's some mistake in that description, we're left to try to guess how many men and women were actually present.
If they had 10 of each sex, and made some other (possibly dubious) assumptions, then the rest of the description works - a woman likes two of the ten men, and each of those two want to see 5 women, which means (this is where the assumptions come in) there's a 50-50 chance each one will include her on their list, and so forth through the rest of it. If the assumptions hold, the numbers seem to work.
If, instead, it were the case that there's 11 men and 11 women instead of ten, those numbers would be 'roughly right' instead of right... and this is what I think they mean, because it leads to 'roughly 50-50' not '50-50', and it seems much more likely they'd think 11 men and 11 women would have '22 separate dates' than 10 men and 10 women could.
So that's my guess. 11 people of each sex, 121 separate dates, on average women want to see 2 (of 11) men again and men on average want to see 5 of 11 women again. Dubiously assuming this all happens randomly, then two men chosen by one woman each have a 5/11 chance of also choosing her, while the five women chosen by one man each have a 2/11 chance of choosing him.
A: I realise this question is from a while ago, but I recently read this article as well and have a slightly different answer.
As often happens when scientific research is "translated" into pop-science-y articles, there has been a misunderstanding.
The original paper reads as such: 
"The average size of an [speed-dating] event is approximately 22 men and 22 women...Striking gender differentials in proposal behavior are observed in the data. In line with sexual selection theory (Trivers 1972; Buss 2003), women are much choosier than men. On average, women select 2.6 men and see 45 percent of their proposals matched, while men propose to 5 women and their proposals are matched in only 20 percent of the cases."
We can see here (and in the following table) that the paper authors intended that the 45% of matched proposals for women and 20% of matched proposals for men is an empirical fact, and not a statistical one.
Statistically speaking, if each of 22 women goes on a date with each of 22 men, and each woman makes two offers, there are two main scenarios I can envision:
(1) Proposals are given purely randomly. This means that if a woman proposes to two men, and each man proposes to five women, the chances that she will be accepted (by either person) is: 2*(5/22) = 45% (Actually it should be 2.6 proposals, but let's use the figures from the BBC article). The chances that any of a man's proposals will be accepted is the same, since both parties have to reciprocate, and under this model, selection is independent and random.
(2) Proposals are not given purely randomly. Then, we need to have some more demographic and selection information to know how to calculate these probabilities.
No matter how you look at it, the BBC article is incomplete and misleading at best. The quoted percentages are empirical, not statistical, as the text would have you believe.
