Did you know

Chatterbox: Down to Earth

Did you know

Did you know that the chance of a CAPTCHA revealing an English word, statistically, is about 1.38%?

This is derived by using the equation of probability:

P = S/E

Where P is the probability of an event occuring, S is the number of equally probable outcomes in which the event would occur, and E is the number of equally probable outcomes in general, event or no event. S would be the number of five-letter words in the English language, and E is the number of total possible CAPTCHAs. A quick internet search yields that there are 164,504 five-letter words in the English language. 

There are 26 letters in the English language. Therefore, there are 26^5=11,881,376 possible CAPTCHAS. We use the probabiliy equation by dividing 164504/11881376, which yields 0.013845534, or about 1.38%. That's pretty small.

My CAPTCHA is thgwz. Not a word. Maybe in about 99 more captchas I'll get a word.

submitted by Sinusoidal Polyglot
(January 12, 2024 - 6:48 pm)

back to the Down to Earth

okay, first of all, I'm pretty sure I only understood 2/3 of that. (so sorry, do NOT have a math-y brain *sigh*) and second of all, that's really interesting! I don't know that (or didn't!!) My CAPTCHA has yet to say a word, and I've been on the CB for 16 months, haha! Still waiting...

But seriously, you are really smart! The way you talk shows how much you take pride in what you know, and you defiently should! I'm always amazed at the things you have to say, because usually you're informing us of something new. Which I usually don't know, and you are younger then me! So ANYWAY, it's just really cool how you have a brain for this stuff. :D 

<iyfuo> Still no luck... :P 

submitted by Hawkstar, age Dynamite, My thoughts in Korea
(January 12, 2024 - 9:01 pm)
submitted by TOPstar
(January 13, 2024 - 8:16 am)

Guess that's my cue to refresh my CAPTCHA 100 times to get one word!

Twilight: ...

Twilight: <dtfwa>? 

submitted by Moon Wolf, age lunars, A Celestial Sky
(January 13, 2024 - 1:20 pm)

that's pretty interesting!

It also does also bring up the question of multiple word CAPTCHAs. For example a two letter word and then a three letter word, or a one letter and then a four letter, etc.

Let's say there's 2 one-letter English words, 124 two-letter words, 1340 three-letters, and 5638 four-letter words. The probability of a one-letter word and a four-letter word would be 2*5638*2/26^5 = ~0.19%. The probability of a two-letter and a three-letter word would be 124*1340*2/26^5 = ~2.80%.

so if we wanted to calcluate the chance of a CAPTCHA "making sense" (i.e. some form of English words, the context doesn't have to fit), it'd be about 4.37%. (if I did my math right...) 

submitted by Hex
(January 13, 2024 - 1:38 pm)

Wow, that's really cool! I did not know that. Thank you for doing the math for us. 

I wonder what the probabilty of it saying a four or three letter word is... It's more likely to happen, right? Because the word wouldn't need all five letters in the CAPTCHA to work...

This is very interesting :)

Alas, Inkling is not saying a word yet ("ytuaz")...

submitted by Rainbow, Holding up the sky
(January 13, 2024 - 2:15 pm)

this is cool! We have, I think, disregarded the possibility of two 1 letter words and a three letter word, as well as three 1 letter words and one 3 letter word and five 1 letter words. Using Hex's method:

2*2* 1340*3/26^5 = 0.00135337859 = ~0.14%

2*2*2*124*4/26^5 = 0.00033396 = ~0.03%

2*2*2*2*2/26^5 = 0.0000026932 =  ~0.00%

Which, added to 4.37%, is 4.54%

Unless I made some arithmetic mistake, which I probably did :) 

submitted by Eclipse
(January 13, 2024 - 6:14 pm)

Ack I forgot two 2 letter words and a 1 letter word, which is: 

2*124*124*3/26^5 = 0.007764 = ~0.78%

so 5.32% which altogether feels too high but perhaps I am missing something  

submitted by Eclipse
(January 14, 2024 - 1:33 am)