'not randomly generated' what does the even mean?!?

[Bat7!]

As expressed in this question:
The telephone numbers for a region of a state have an area code of 570. The next seven digits represent the local telephone numbers for that region. A local telephone number cannot begin with a 0 or 1. Your cousin lives within the given area code.
What is the probability of not randomly generating your cousin’s telephone number? Explain.

I understand the denominators - one 8 and 10 to the sixth power - but not the numerators. I don't understand why the chance of randomly generating a number and the chance of NOT randomly generating a number are the same thing... (are they the same thing???)

Thanks in advance!

 

[hlsmith]

I would imagine they are compliments (e.g., 0.9 and 0.1). So if you have a value you just subtract it from unity (1) to get the other.

 

[Bat7!]

I thought that for a moment - like P (1-P) but how would you solve this question?

 

[hlsmith]

This will be likely an incorrect answer, but if you had a 7-digit telephone number, that would mean you have 0000000-9999999 as options. So 10M possibilities. Selecting the target number by chance would have a 1/10M chance and not selecting it would be 9999999/10M.

 

[Bat7!]

Thanks for your help...