Originally posted by LarryJs
If I teach a monkey how to hit the keys on a typewriter in a random mannner how long will it take said monkey to produce the complete volume of shakespears works?Don't know?
I will answer the question myself then:NEVER it can't happen
The probability surpases 10 to the 40th power(the borderline for a questioned event to happen in 10 billion years ,it was set I think by Emile Borel maybe someone else knows)
Emile Borel, Probabilities and Life
Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation.
That says it all, I guess...

Originally posted by Larryjs
The 10to the 40th limit is set
by the currently accepted age of the universe at 10 billon years.
The monkey could not complete the works because he doesn't have enough TIME (Let's just say this hypothetical monkey is immortal or very nearly so)
I'm following you there, Larry, but it doesn't make sense...
Your original question is misleading ('How long will it take'): that's a question that can't be answered - it depends on the monkeys' typing skills, and on other variables that we don't know...

Therefore: The 'time'-factor is of no importance here. The only question that matters is 'Will the monkeys eventually produce it, yes or no?'. Sure it's unlikely, but given enough time and enough monkeys, it WOULD happen. That's why the time-factor isn't important: let's say chances that one monkey will produce the complete Shakespeare oeuvre are 1 out of 10 ^40. Now, what are the chances if we gave 10 ^ 40 monkeys a typewriter?

Right...
Never underestimate the power of 10 ^ 40 power monkeys

BUT - and this is where I agree with Larry - there's something we are missing here, namely the HUUUUUUUUUUGEness of the problem.

Lemme try to explain:

Let's say all the monkey has to type is 'Hamlet'

The math is easy: there are 26^6 possibilities with a 26-letters-keyboard: 308.915.776 possibilities that is. Let's say the monkey can produce one 6-letter word every second. The math is easy again: that's 31.556.736 6-letter words a year. So the answer to that question is easy: the monkey will NOT produce the word 'Hamlet' within a year, no doubt about that (even if every word he produces is different from all the previous ones). Problem: there IS a chance he WILL produce the word, but it's tiny

Let's look at it from another point of view: let's calculate the chances of the monkey producing that word in one year by calculating the chances of missing on every attempt - reverse mathematics, if you will
The chances of getting that word will be 100% minus the chances of missing on every attempt...

The chances he misses at his first attempt = 1 - 1/(26^6)
The chances he misses all his attempts for a full minute = 1 - 1/(26^6) ^ 60 and so on untill:
The chances he misses all his attempts for a year straight = ((((1 - 1/(26^6)) ^60) ^60) ^ 24) ^ 365

My l33t Windows calculator fails on me here though... (Maybe someone can try it on a Unix-box)

But what's the point of all of this? The output of this equation will be something like 0.9999999999....xxxxxx , meaning the chances the monkey will NOT produce that word are almost 100% . Even if we use 10 ^40 billion monkeys, the outcoming would always be something like 0.9999...xxxxx ! Meaning those monkeys will NOT produce that one damn word

Just some thoughts...


BTW: there's something wrong with the logic in that last example

This entire discussion reminds me of my little brother: 'I wanna go to a casino: either I win, or I don't win. So I have 1 chance out of 2 to win.'

PS: I don't have a little brother. He's 23.