On meeting 'otiose' twice in a day

Well, not in the same day, but certainly within a 24-hour period. As I was lying in bed last night, reading Charles Mann's 1493, I came across the phrase the otiose Percy on p. 78.

As of this morning, I've read to p. 90, so that's about 4,500 words later. I also read a few NY Times articles, adding perhaps another 1,200 words. And then I set about to edit an article for Contact, the TESL Ontario magazine for which I'm the editor. Almost immediately, I came across a quote from David Crystal in which he wonders,

whether the presence of a global language will eliminate the demand for world translation services, or whether the economics of automatic translation will so undercut the cost of global language learning that the latter will become otiose.

So that's twice in about 6,000 words. What are the chances of this? [See the update]

Well, not liking to leave rhetorical questions hanging, I set out to see. The adjective otiose (roughly meaning "of no value or use") occurs at a rate of 0.03 times per million words in COCA. That's about once every 32 million words or so. Google Books put it at a higher rate: one in 10 million. So let's say my chanced of meeting it are about 1 in 15 million words (0.00000667%).

As I say, we're looking at a window of 6,000 words, so we divide 6,000 by 15,000,000 to get 0.0004. Multiply this by the original odds to get a 1 in 37.5 trillion (0.0000000027%) chance of meeting otiose once in a span of 6,000 words.

My odds of doing that twice in 6,000 words (assuming these are independent events, which is more or less right) is simply the odds of doing it once squared. So, that's about 1 in 1.4 sextillion.

So that's, like, wow!

But.

That's the odds of me doing it in this particular stretch of 6,000, not the odds of some person doing it some time.

Let's say the average English reader reads 10,000 words per day and there are about 300 million people who read English. That's about 30 trillion words per day. So—this is where I lose confidence that I'm getting the reasoning right—the odds of some English speaker reading otiose twice in the span of 6,000 words is about one in 4,687,5000 each day or one in 128,000 per year.

Given that, I think it's most likely that no other person has ever accomplished this feat.

Except you.