one addition to that:
if you take a dice and dice a lot of times every number usually occurs equally often. you need a lot of bad luck to never dice one of the numbers with 6 choices: still it's possible.

but if you take a infinite sided dice: it is a whole other story. thats were the funny assumptions start.

but(to be clear): if you have a /set/ of numbers you want to see dicing with the infinte sided dice you have a good probability that one of the numbers from the set occurs if the set is /big/ enough. the bigger the set the better your chances to see one occur even with finite tries. and with the monkey: it's higher for every "letter" comes from a finite set. and you can give a finite set of combinations that may occur trying to form your "word". say the word is "eat". then you have codesize^3(ascii would be 255^3 ) combinations which is finite. with such finite probabilities you can calculate(thats a lower limit for the prob. , taking the "n out of m" in addition to that prob. increases a lot ...) . so you can give a probability but you don't know if it occurs even with infinite tries.