Eli5: What’s the difference between something with 1 in a million odds and 0 in a million odds?

Question

I was thinking about lottery odds, and how so much of the pitch is, essentially, you miss 100 percent of the shots you don’t take, with the thought that you should at least enter because your odds go up so much with just one ticket. The odds were non existent before, and now they exist even if they’re vanishingly small.

Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million, or between 492,368 in a million vs 492,369 in a million? Or are all three of these functionally the same?

In: 0

Answer 1

Imagine you have a nuclear plant. This nuclear plant has a flaw, every minute, it has 1 in a million chance to explode. How safe is it? The answer is not at all, because a “1 in a million every minute” means “it will explodes within 2 years in average”.

Imagine that that commercial planes had a 1 in a million chance to explode each travel. That would be roughly 30 plane exploding each year.

In other words, “1 in a million” matters when you deal with large scale. Large number of peoples, large amount of time, etc.

> Is the difference between 1 in a million and 0 in a million actually somehow more than the difference between 1 in a million and 2 in a million, or between 492,368 in a million vs 492,369 in a million? Or are all three of these functionally the same?

Numbers that are functionally the same in practice are numbers that have the similar “logarithm”.

For numbers bigger than 1, that means counting the number of digits in front of the decimal: so 1-9 is roughly the same, 10-99 is roughly the same, 100-999 is roughly the same, etc. Obviously, the limits are arbitrary, and if you want to be precise, 99 should be more similar to 100 than to 10, but that’s a good enough approximation.

For numbers between 0 and 1, that means counting the number of zeros before the first non-zero digit. So 0.1-0.9 is roughly the same, 0.01-0.09 is roughly the same, etc.

So 1 in a million and 2 in a million are functionally the same, but 1 in a billion would be fundamentally different.