Hi, I'm just doing some personal problems and I ran into this thought...

Take for instance this passphrase: "dog.cat.mouse"

(which is inclusive of the periods but exclusive of the quotations, so a total of 13 characters)

The goal is to guess this passphrase, using the set of American English alphabet, both lowercase and uppercase, positive numbers 0-9, and the following symbols: [ ] \ ; ' / , .

So that's a total of 70 characters.

A total of 30,000,000,000 (thirty billion) guesses are possible every 1 second. The length of the passphrase is unknown.

The question: what is the probability that this passphrase will be guessed within the time period of 500 years?

The only way I could think of approaching this problem would be to find the probability of guessing the passphrase within a second, then calculate the number of seconds in 500 years, and then multiply the previously aforementioned probability with the probability of guessing it in 500 years? I'm not sure...

How would I go about this?