Password Guessing

Passwords are an important aspect of computer security. But how secure are they, really?

First off, way too many people use passwords that are easy to guess.
(Think birthdays, child names, pet names,)
And many of those who use better passwords, habitually write them down, and leave them near their computer.
And remember, if you use a ‘password vault’, if you crack that ONE password, you have access to ALL of the rest.

But how long would it take to guess a password, using a computer?

Assume for the following discussion that a computer can guess 100000000000 passwords per second.
https://theconversation.com/a-computer-can-guess-more-than-100-000-000-000-passwords-per-second-still-think-yours-is-secure-144418

You may use a calculator, but you must show how you got your answer.

EXAMPLE
Assume you know a password is exactly 8 characters long, and all lower-case letters.

26^8 = 2.08827E+11
2.08827E+11/100000000000 = 2.08 seconds

Well that does not sound very secure.
How about 8 character passwords, upper AND lower case?

ANSWER____

But, most people, if you allow capitals, only capitalize the first letter.
How about 8 characters, but the FIRST letter might be capitalized?

ANSWER____

OK, what if we add numbers?

How about 8 characters long, upper or lower case, or digits?

ANSWER____

BUT, be realistic.  How many people mix upper and lower case randomly?

OK, how about special characters?

Assume for convenience you allow for 10 special characters.

OK, with 26 lower case letters, 26 upper case letters, 10 digits, 10 special characters:
8 character randomly generated password.

How many?

ANSWER____

But how many people can remember even an eight-character random strong password?

For further thought:
More and more, secure passwords either use two factor authentication (even VSU is now requiring that for campus web pages), pages that lock after a few unsuccessful attempts, et cetera.