Another throw of the dice

A little probability conundrum.

About twenty years ago, I worked in a very sociable office. The camaraderie was great and we tended to do team dinners and so on. One of the team was a young man, a delightful carrot-top, in the "sandwich" year of his degree. He went back to university but stayed in touch. We bumped into each other occasionally in the nineties but lost touch by about 1997.

Last week we made contact through a business social networking site. We exchanged a few catch up emails and shared family photographs. Carrot-top remembers my children when they were youngsters and was stunned to see photographs of them all grown up. I was delighted to see his wonderful red haired genes have appeared in both his daughters.

He suggested that, the next time I was in his neck of the woods, we should catch up for lunch. Turns out we share the same neck of the woods. In fact, the same tree. Carrot-top works at Number 55 and I work at Number 82.
We laughed. A coincidence.

We met for lunch and rabbited away like crazy with a dozen years' of catch up. I brought him up to date on my children's growing up years. My son, a physicist, studied for his first degree at the same university as his brother teaches. Physics.
We laughed. A coincidence.

Carrot-top enquired if Junior Mad had ever had anything to do with the particle physics side of the department. Not for his first degree, I replied, but funnily enough ... The penny dropped. Dr Carrot-top. Carrot-top's older brother. Senior Research Fellow. Dr Carrot-top. Supervising Junior Mad's PhD.
We laughed. A coincidence.

Care to work out the probabilities? Some of these factors are independent and have no link at all to each other and others are connected.

The likelihood that, if we met again, we would work out the coincidence, would be close to 100%. Not definite, but close. Say 95%

That my son went to university in the first place? Probably close to 100% again, given his background. It's close to 40% for the wider population but we know that children of parents with degrees are more likely to go into higher education. Let's call it 75%.

That my son chose to study Physics? A relatively unpopular subject. Say 5% out of the total of subjects studied.

That his brother and my son are are at the same university? There are 85 universities in the UK teaching some sort of Physics. Slightly less than 1%

That his brother supervises my son? About 10% of Physics graduates go on to do a PhD. Quite often they stay at the same insititution. Say about a quarter. Again connected to the whole university and physics thing above.

That we should work so close to each other? We were in the same field twenty years ago so we would be more likely to be working in the same area. There are roughly 120 streets / zones where we would be likely to work. Less than a 1% chance.

Just on my fingers and toes, it's about 1 in eleven million. Still, better odds than doing the National Lottery.


You didn't know I had that many toes did you?