Help with probabilities?

Question

Hello, I need help with this question. I keep on coming up with different answers each time so I need someone to confirm an answer. Here is the question:

 

United States telephone numbers consist of a 3-digit area code, a 3-digit exchange, and a 4-digit station number.

 

A. Suppose that, while someone dials a number to your area code and exchange, the last two numbers are accidentally transposed. What is the probability that the wrong number dialed is your number?

 

B. Suppose that, in another case, someone incorrectly dials the area code in a long distance call (in the United States). The exchange and station number happen to match yours. What is the probability that the number dialed is your phone number? (Note: Even though some area codes are not valid, for example, 000, it is still possible to dial these numbers).

 

I need the answers to both parts please. Any help would be appreciated!

Answer 1

This is more a reasoning problem than an algebra problem.

 

A)

The only digits that matter are the last two (all else is extraneous information).

The last two digits have 100 pairs, 01 - 99, and 00.

Ten of this are the same as the transposition: 00, 11, 22, ...

So only 90 are different if transposed

The provability is 1/90.

 

B)

1000 combinations are possible for the area code: 001 - 999 and 000.

The probability is 1/1000.