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Comment by kbrkbr | Hacker News Reader

> You’re about 90% sure you know how to start the app. You’re 80% sure you know how to handle the infra you’ll need to get it online. And you’re 70% sure you know how to get your first customer. What is your chance of successfully going from zero to first customer? 0.9 * 0.8 * 0.7 = a little over 0.5.

This would be true if the probabilities were independent [1], which they are probably not, as the infra is tied to the app.

The probability can be anything from 40% to 70%. You can see that if you arrange 3 rectangles inside a unit square, one with 90% of the size, one with 80%, one with 70%. If they contain each other, their overlap is 70% of the whole, namely the smallest rectangle. In the worst case it is 40%, when the 80% is 10% out of 90%, giving 70% overlap. And then 70% is 30% out of that overlap, leaving 40%.

[1] https://en.m.wikipedia.org/wiki/Independence_(probability_th...

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You're not wrong, mathematically. But these numbers (90%, 80%, 70%) are made up, so it's kind of irrelevant whether we're doing the maths right or not.

Yes, the confidence interval on the model which assigns the probabilities is so large, any confidence on derived conclusions here is pretty meaningless.

Quite the contrary. The only thing that really matters when it comes to probabilistic forecasting is that we do the maths right.

The numbers will always be made up estimations, so the only thing that sort of makes sure we converge on similar solutions is getting the maths right.

A person is free to make any outlandish estimation of any individual probability, but when they are faced with the task of trying to make it mathematically cohere with other estimations is when they realise how outlandish the initial estimation was.

I have tried to write about this before: https://two-wrongs.com/what-is-probability.html

Ok, from reading the first section of your post:

> Events need to be well defined

Then from the article:

> Say you’re working on a Laravel web app. You’re about 90% sure you know how to start the app. You’re 80% sure you know how to handle the infra you’ll need to get it online. And you’re 70% sure you know how to get your first customer.

Are these events well defined?

1. Starting the app (about 90%)

2. Handle the infra (80%)

3. Get your first customer (70%)

3. is possibly well defined, or could be made so. The others are not. So not only are the numbers made up, the events are not even well defined in the first place! Why would we go to the effort of ensuring correct maths here?

I'm going to give OP the benefit of the doubt and assume they have sat down and figured out what "starting the app" really means, but they didn't want that definition to be the focus of the article.

Correct, it would be better read as P(app start) * P(infra ok|app start) * P(first dollar|infra ok and app start). That's just a mouthful so I elided the "givens".

This is usually the easiest way to estimate these probabilities also. Thanks for elaborating!

Yeah, that makes sense! Thanks for pointing out

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