License plate number probability

I have a real life probability question.

California license plates are 7 digits.

This actually happened:
My sister received a randomly assigned plate about 8 years ago and still has it.

Recently our mother received a randomly assigned plate as well, she's had it for a few months.

Today we noticed that the two plates are just one digit off. Not only that, but the digit is just one letter off. I won't use the real numbers, but as an example:
Sister's plate: 1BD0123
Mom's plate: 1BE0123

They are not associated as far as the DMV is concerned, have different addresses and last names, and live in different cities.

So, my question is what are the odds of that happening?

Mean Joe

TS Contributor
It depends on the number of possibilities there are for each "digit" in the license plate.
You should probably restrict the number of possibilities to only what has been released in the last 8 years (eg the first "digit" could have up to 10? possibilities as it could be any numeral 0-9, however in the last 8 years maybe only 3 of the numerals in the first "digit" have been released).
Multiply the 7 possibilities corresponding to the 7 "digits". That's your denominator.
Your numerator would be (more or less) 2*7 -- 2 comes from being off by just one digit (either above or below), and 7 comes from having 7 digits where that miss could occur. It might actually be less than 14, if certain digits haven't been released in the last 8 years, or for example if your sister has the digit 0 in her number and then the only "one off miss" could be 1.