The serial number on a $10 bill contains eight non-zero digits. If your $10 bill contains the digit 7 at least once, you win a prize. The probability that your $10 bill will be a prize-winning bill is what?

Answer 1

I believe I answered this in an earlier post.

There are 9 possible values for the first digit and 9 for the second, and so on. So, there are 9^8 possible serial numbers, where no digits is a zero. Similarly, there are 8^8 possible values where no digit is a zero or a seven. So, the probability there is at least one seven is:
1- (8^8)/(9^8)