Gainsley
You are absolutely right about the chances. However, in my same tour at Midland Radar we had another mid-air collision. A Varsity on a 'navex' with student navigators and some air cadets on board.
As I recall, the Varsity was transiting noth bound under airway Blue 1 somewhere in the vicinity of RAF Lindholme and was under a limited service due to the base of cover. I believe the Varsity was flying just on top of cloud cover. It was hit by a light aircraft climbing through the cloud (not working Midland Radar). The pilot of the light aircraft was killed ( I think an Army Major). Subsequent to the collision, I think the Captain of the Varsity claimed to have fallen out of the aircraft supervising the bail out of the crew. Sadly, an air cadet bailed out and then died after falling out of his parachute.
The Varsity was landed by the Co-pilot assisted by a student navigator in a field but hit a solitary tree ..I believe with no further fatalities.
This and the previous Victor/Canberra accident rather dented my belief in a mathematical model presented by a Flt Lt Bob Addreley while I was a student on the Joint Area Course at RAF Sopley (Yes, I am a knackered Old **** !). Bob's theory was that ' random track selection' was the best method of reducing the chance of a mid-air collision. Please bear in mind that at the time of his 'model' most airways were only 10 miles wide and military flying generated a huge amount of traffic.