### Some musing on the nature of probability.

A mathematics student is about to board a plane when the bag check reveals that he is carrying a bomb in his bag. Arrested he is taken away for questioning. Why is he carrying a bomb?

It is quite simple, he explains, have you never heard of the multiplication law for calculating the combined probabilities of independent events?  He goes on to explain that this is mathematical term relating to the likeliness of two independent events occurring. The compound probability is equal to the probability of the first event multiplied by the probability of the second event.

If the odds of there being someone on a plane with a bomb are 1/1000, then the probability of there being two bombs on the plane = 1/1000 x 1/1000 = 1/1000000.  so I feel much safer!

[At this point if this were a maths blog we would discuss the nature of independent events as by bring a bomb onto the plane then you would really want to calculate the conditional probability of there being 2 bombs on the plane given that there is already one, but I digress.

I and my much better half met up with a friend who I hadn’t seen since my days with Team Talbot Guildford. about 30 odd years ago ( I am spectacularly bad at keeping in touch with people). Apart from our connection with the team we have something else in common.  You don’t need to exercise the ‘little grey cells’ in the manner of Hercule Poirot to guess what it is, given the nature of this blog.

So on the way home, as with my much better half driving, we ascended the steepest road I can ever recall being driven up, outside of the Scottish Highlands, or indeed driven down (as on the way there, when it resembled a ski jump for cars, as in some wacky stunt from the BBC TV show ‘Top Gear’), I pondered to distract me from the slope, on the odds of two out of a group of fourteen (10 players, coach, assistant coach, manager and statistician) developing Parkinson’s.

Back home I started to look up the odds of one person developing Parkinson’s

• Read this bullet point if you are OK with mathematics: so I could apply the binomial distribution to the numbers.
• Read this bullet point if you are a bit afraid on mathematics: blah blah blah omg numbers look away now blah blah.

And that is where it got interesting. Did you know that an Amish welder, with red-hair who was an exponent of the pugilistic arts and has a history of Parkinson’s in the family stands a greater chance of developing Parkinson’s than the man on the Clapham Omnibus.  (Unless I suppose the red-haired Amish welder and part-time boxer who had a relative with Parkinson’s was visiting London and had caught a number 88 bus.)

HERE is a link to a really interesting article about  factors affecting the incidence of Parkinson’s Disease. This was a lucky break, Sherri Woodbridge’s Parkinson’s Journey is a fantastic blog about Parkinson’s Disease

WARNING! SERIOUS MATHS APPROACHING. SKIP THIS BIT IF YOU WANT.

So what figure can I use?  Here are some numbers from the Parkinson’s Disease Foundation website.  More than 1 million Americans suffer from PD and it is estimated that more than 10 million people worldwide are living with Parkinson’s disease.

The population of the USA was 321.4 million in 2015.  So an estimate for the odds of a person developing PD is (very) roughly  1 million ÷ 321.4 million = 0.00311139

Let’s just call it 0.003 as it is a best an educated guess.

I’m going to treat the as a binomial distribution.
There are 14 people in the minibus  so  n = 14.
The probability of developing Parkinson’s  p = 0.003
so the probability of not developing it is     q = 0.997
The probability of 2 people out of 14 developing Parkinson’s is
14C2 x (0.003)² x (03997)¹² = 0.00078999… or approximately 0.0008

NON MATHEMATICIANS YOU ARE SAFE TO READ AGAIN

So the probability was 0.0008 or put another way 1 in 1250
Of course this is all based on my original estimate which, let’s face it was just one step removed from a wild guess. The second most important thing is that I got the chance to crunch some numbers and exercise my brain.

The most important thing was, of course, meeting my friend again after all those years.