Crtd 12-05-16 Lastedit 14-08-20

Summary: under a gender ratio equality constraint among candidates for 34 posts, the chance that some (any number between 1 and 17) best candidates for a ministry are rejected for reasons of gender discrimination is 86.4% . But the possible bad luck is exactly alike for females and males.

If Hollande went for the exact 50% of female (and thus of male) ministers, if capacities differ but sex is totally unrelated to capacity, then what is the chance every one of the 34 new French ministers is the best for each of the 34 minister-posts?

The math:

How many ways can only one female be the best for one ministry, the other 33 ministries having a male best candidate? 34. And when there's two such ministries where a female is the best candidate, in how many combinations could that be? 561 (34 x 33/2). Now 17, half-half exactly?

We have calculated three examples. Now add up not just those three, but all possibilities there could be from 0 females the best for a post to: for all post the best happens to be a female. That makes

Are all these possibilities equally probable? They are! For though capacities differ over candidates, these are totally unrelated to whether the candidates are male or female.

What is the chance that having the best on each post would result in a 50% male, 50% female appointment exactly? This first number divided by the second:

That means the chance that some (any number between 1 and 17) best candidates for a ministry have been rejected for reasons of gender discrimination is 100% - 13.58337596% = 86.4......% . But the possible bad luck is exactly alike for females and males .

(I seem to be wrong cause I sent it to BBC WorldService and it was not read. Or of course everybody already knew so no need to broadcast).

Exercize 1: at the constitutional dinner ministers and Hollande all clink each others' glasses on the new cabinet. How many clinks? French cabinet ministers better just count, others: calculate!

Exercize 2: How many clinks between a male and a female?