Written by Colin+ in probability, sport.

Former Formula 1 driver @MBrundleF1 asks:

These election opinion polls. I've never been approached, nor has anybody I know, about a poll on anything whatsoever. Who are these people?

— Martin Brundle (@MBrundleF1) April 5, 2015

(Obviously, he didn't ask *me* specifically, but I thought it was a good question.)

From a pragmatic point of view, to be in a phone poll, I'd presume you'd need to have your phone number available for people to ring, you'd need to answer calls from unknown numbers, and you'd need to not hang up when someone says "I'm Hughie from IPSOS MORI, do you have a few minutes to answer some questions?" I'm nowhere near as busy as Mr Brundle, and the chances of a pollster getting through to me are pretty slim. (Also, being an F1 enthusiast, I'd imagine he spends quite a lot of his year overseas watching motor-cars go brm brm. Not my cup of tea, but different strokes, etc.)

However, let's ignore pragmatism1, and suppose we're in the kind of world where pollsters pick people at random from the electoral roll and stop at nothing to get hold of them. How likely is it that a particular voter would never get picked?

OK, let's make some assumptions: taking a ballpark figure, I'm going to say that there are 10 national opinion polls a month. Martin Brundle is now 56, so has been a voter for 38 years, and thus eligible for 4,560 opinion polls. (In likelihood, there were fewer opinion polls when he was younger; however, I want to make conditions as favourable as possible for Brundle to give his opinions -- so let's say no more than 5,000 polls.)

What's the probability that a random person wouldn't be picked for any of them? Let's see: there are currently about 46 million voters in the UK; in 1974, Brundle's first election, there were about 40 million. I'll use that, because it's easier to work with, and again because it's favourable to Brundle.

The probability of being picked for any given poll is 1,000 in 40,000,000, or one in 40,000. The probability of not being selected over 5,000 polls is $\left( 1 - \frac{1}{40,000} \right)^{5000}$ -- the Mathematical Ninja says that's about $e^{-1/8}$, or about 0.88; the calculator says 88.25%, almost bang on.

That is to say, under favourable conditions, someone available for polling for nearly four decades would have roughly a one in eight chance (11.75%, if you prefer) of being in a survey. In reality (because of my generous assumptions), the probability is smaller still.

- As well as the assertion that nobody he knows has ever been asked -- I find it hard to believe he's asked
*everybody*he knows, or that everybody he knows remembers every annoying phone call they received in, say, 1983 [↩]

## MathbloggingAll

An ex-Formula 1 driver asks… why does nobody ever ask me my opinion? http://t.co/CJ3SPe4cX8

## math1teacher

RT @icecolbeveridge: [FCM] An ex-Formula 1 driver asks… why does nobody ever ask me my opinion?: http://t.co/ApnH2jbrG2