I forgot the last digit of a 7-digit telephone number. If I randomly dial the final 3-digits after dialing the first four, then what is the chance of dialing the correct number?

$\frac{1}{1000}$

It is given that last three digits are randomly dialed.

Then each of the digits can be selected out of 10 digits in 10 ways. Hence required probability = $\frac{1}{1000}$