What are the odds

Anything unlikely happened to you recently?

I drove home yesterday and someone both my front headlight bulbs have gone. They go relatively frequently, compared to other cars I’ve owned, but what are the chances of both going?

The other day in a restaurant I was posing for a photo with the lads and I inadvertently did a nazi salute at the waiter, despite never having heard of the nazis, let alone knowing what their salute is. Also the guy I was directing it at has a name that rhymes with mussolini. What are the odds?!


Nerd voice Well it’s actually fairly likely they would go at the same time, considering they would both have been installed at the same time, have the same amount of use and the same average lifespan


dropped my passport and someone handed it in the police

the odds were 73/1

This. Similar fault failures are very common place

Nah - It’s an eight year old car. They’ve both been replaced individually numerous times.

I just ate an Punschrulle and now I want another one.

That is not how statistics work. However if you said it could have been an electrical fault, I could get on board.


But they would have both been installed at manufacture, and they both have the same standard lifespan, even if one goes first, it’s only a matter of time before the next one does, and at some point the chances are they’ll go together.

Well, you make that argument, but have you ever spoken to anyone else in your life that this has happened to?

:raised eyebrow emoji:

I have spot lights in my kitchen, and it’s never just one going, it’s always multiples, and I know when it happens to stock up because they’ll all be on their way out soon.

I’m not talking about your kitchen, I’m talking about people’s cars!

Had my car about 4 years, changed just one singular headlamp in that time. I always assumed that was normal, but is this actually the improbable option?

Seems to me like both headlights going at once is more improbable, but idk why.

So I’ve a D20 in each hand right. And if I roll each simultaneously D20 until I get a 20, each has the same probability of getting a 20, but if it happens for each on the same roll, that’s less probable than on different rolls yeah?

Gonna think about this all day, I hope one of you will apologise to my boss for destroying my productivity.

Since they’re two separate dice (or two separate headlights), the joint probability should be treated as independent events:

If two events, A and B are independent then the joint probability is
P ( A and B ) = P ( A ∩ B ) = P ( A ) P ( B ) ,
for example, if two coins are flipped the chance of both being heads is 1/2 × 1/2 = 1/4

So, if the odds of a headlight going were say 1/100, then the odds of both going are 1/100 x 1/100 = 1/10,000

Yeah but the whole point was that they might not be independent events.

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years ago my Dad drove a red ford granada estate. 20 odd years after he died I was in Bournemouth with my Mum and was in the area of my Gran’s house (also long since dead) where my Dad grew up, so thought would just pass by the house to see if anything had changed. Parked outside was a Ford Granada Estate (weirdly can’t remember if it was red though).
Hadn’t seen that car make in 20 years, never seen one since.

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Can any two events ever be truly independent of one another?

In my opinion, the language used in the original assertion implies they are statistically independent events. Note ‘average lifespan’ which immediately brings the reader to consider Poissonian statistics.

My response, below, implies your statement, yes.