[grayclhn]

To be super pedantic, for one million ops it's closer to a 63% chance every day:

Pr[something happens across 1_000_000 events]

= 1 - Pr[nothing happens across 1_000_000 events]

= 1 - Pr[nothing happens once]^1_000_000 ## assuming independence

= 1 - (1 - Pr[something happens once])^1_000_000

= 1 - (1 - 1/1_000_000)^1_000_000

≈ 1 - 0.378

= 0.632

It's still below 99% for 4 million ops.

[Dylan16807]

> for one million ops

Okay, but they said millions.

> It's still below 99% for 4 million ops.

I find this misleading, because it's... 98%.

Which completely undermines your argument. If something happens 98% of days, it's fine to call that "every day".

[grayclhn]

Dude, it was meant to be mildly educational, not an "argument."

[Dylan16807]

Then present it as a fun fact rather than as a correction?

And I'm not trying to be mean but I think the way you phrased your last line is accidentally anti-educational. Your last line treats 1 million ops and 4 million ops as nearly equivalent, when the truth is that 1 million ops is far from "every day" while 4 million ops can easily be called "every day".

And if you dislike the word "argument" pretend I said "point"? I think you're reading connotations into that word that I didn't intend.

[grayclhn]

And yet... here you are, having applied that same mathematical principle to calculate the probability of observing a one-in-a-million event at least once in 4mil independent trials. That's probably something you already knew how to do, but if not, it's a pretty educational moment. ;)

ps — "to be pedantic" means "fun fact" but sarcastically.

[Dylan16807]

The bulk of your post was educational, but it was misleadingly shown as an answer to both "million" and "millions", when those two scenarios actually have very different answers.

> ps — "to be pedantic" means "fun fact" but sarcastically.

It means that, but also sets it up as a correction. But "millions" being "every day" was right all along.