maxman
Top of my head - there are 200,000 doctors registered with the GMC and the UK pop is around 60,000,000, making 1 in 300 people a doctor. So on a reasonably full 747, so you'd be rather unlucky not to find a doctor on board.
In reality, I would guess that more doctors fly than the average member of the population, so the odds are really somewhat better than this.