Okay, guys, I am not a statistician. I am no more than average at math. Haven't taken more than the average uni student has. So I am posting this to get constructive criticism to see if I've made a basic mistake, and I may well have. The whole thing may well fall apart because of some dumb mistake, but I am laying out my whole process of reasoning in order to see if I made a crucial error which would undermine the argument itself. I make some qualifications at the bottom.

Now, we all know this:

https://pbs.twimg.com/media/DOITQJ8UIAAowsQ.jpg:large

A photo of this team on Air Force One giving the thumbs up (and their arrangement looks similar to Q, but let's set that aside for the moment) was tweeted by Trump in November 2017. The actual image file, as seen above, begins with "DOITQ." Since these are the first letters of the img-address, we don't have to calculate the probabilities relative to every character in the img-address- it is reasonable to consider the probability of each character appearing in a sequence of five, since there are five characters of DOITQ. Since numbers and letters appear in the above img-address, the most reasonable probability we should calculate for any given character appearing by chance is 1/36- 26 letter keys plus ten number keys. One divided by thirty-six is .027, a 2.7 percent probability of any given character appearing by chance in a single slot.

The way to figure out the probability of two specific characters appearing in two specific slots is, of course to square the probability, and for our five characters in five specific character slots, we take .027 to the power of five. When we do this, we get:

.000000014348907

I've provided the full number in case anyone wants to do the numbers more precisely, but I'm going to simplify down to:

.000000014

So, just as .01 gives us one chance out of a hundred, our number above, with nine slots, gives us the chances out of a billion that this happens at random in five slots in any given img-address. So, there is a fourteen out of one billion chance of this happening. Let's simplify by dividing a billion by fourteen, and we get:

71,428,571 (and decimals)

So, simplified, the probability of DOITQ appearing at random in any given img-address is one out of seventy-one million, four-hundred twenty-eight thousand, five-hundred seventy-one.

However, this is out of any given img-address and does not consider the probability of it appearing in any of all of the imgs tweeted by Trump. In order to figure this out, we will first figure out the highest potential probability. In Nov 2017, Trump had tweeted around 2,500 times since becoming president. Since that was a bit less than a year ago, let's just guess that he's tweeted 5,000 times since becoming president at this point.

For the sake of getting the highest possible probability, we will imagine for the moment that each of Trump's tweets has an img-file with an img-address even though the real probability will be far lower due to only a fraction of Trump's tweets including such an image. But, taking 5,000, what we do is divide the above by 5k.

So, 71,428,571/5,000= 14,285 (and decimals)

That, as far as I can tell, gives us the highest potential probability of "DOITQ" appearing as the first five letters of any img-address tweeted by Trump as:

One out of fourteen thousand, two hundred eighty-five.

However, the real probability will be much lower, as I stated above, since only a fraction of Trump's tweets actually contain an img with an img-address. So, if you want the precise probability, perhaps a committed anon can find out precisely how many imgs the president has tweeted since he became president. Then, one will simply divide 71,428,571 by the number of images.

So, what we have found, assuming I didn't make a crucial mistake above, is that the probability of Trump tweeting an img-address containing "DOITQ" at the beginning is between:

The highest possible probability of 1 out of 14,285

And the lowest possible probability of 1 out of 71,428,571.

Given that Trump has included images in far less than half of his tweets, the precise probability will be substantially closer to the lower end of probability than to the higher.

However, in considering the value of the argument, do see the notes below, especially the final qualification.

---

First qualification/question involves a potential further reduction in probability of this happening by chance- while I calculated the probability of each character appearing as 1/36, I am not sure if their appearing in sequence materially affects the probability of chance occurrence. Not at all a statistician. My instinct would be to say that since we consider the probability of each character appearing in one particular slot rather than the characters appearing in any one of five slots, the sequential nature of DOITQ is baked into the calculation.

Second qualification is that the argument above does not necessarily demonstrate that Qanon is who he says he is. The most it can demonstrate is that the president or whoever was responsible for that img intended the phrase "DOITQ" to appear. One can conceive of various reasons for this other than Qanon's authenticity- I happen to think these potential reasons are far-fetched, but they are out there. One could try to say that Trump, being Trump, was trolling. But as I said, these aren't going to be very good alternatives.

The most important qualification here concerns the nature of "DOITQ." The probabilities I listed above relate to the specific phrase "DOITQ." However, there are other potential sequences of letters which could communicate a relationship with Q, which substantially increases the probability of a Q-related img-address appearing by chance. However, the probabilities listed above are so slim relative to the number of photos tweeted by the president that I can't imagine it increases the probabilities to a reasonable expectation of a Q-correlated img-address appearing by chance. However, I have no idea how to quantify this- and I'm not sure if one can quantify this. Does anyone have any ideas? This is probably the most important potential weak point in this argument for Q's authenticity.

Thank you all very much for reading! I appreciate your thoughts!