TITLE: Number of 6-digit passwords, starting with even or ending with odd digit
QUESTION [7 upvotes]: My problem is

A password consists of six digits, each in $\{0,\ldots,9\}$
  How many passwords start with an even digit or end with an odd digit?

the answer is $750,000.$
I would like to know how exactly do you get $750,000$ as the answer?

REPLY [2 votes]: I was hoping to see a simpler answer, but instead I guess I'll supply one.
There's a 50% chance of the password having an even first digit.
There's a 50% chance of the password having an odd last digit.
Therefore, there's a 25% chance of the password having neither, and a 75% chance of the password having one or the other.  
So, for 6 digits, the answer is 750,000.