You correctly dial the first four digits of a 7-digit telephone number but have forgotten the last three. If you dial the last three digits at random, what is the probability of dialing the correct number on a single attempt?

Introduction / Context:The last three digits are unknown and assumed equally likely across 000–999. A single random attempt has success probability equal to 1 divided by the number of possibilities.

Given Data / Assumptions:

• Three unknown digits, each 0–9.
• Total combinations = 10^3 = 1000.
• Exactly one correct triple.

Concept / Approach:Uniform discrete probability over 1000 equally likely outcomes, with one favorable outcome.

Step-by-Step Solution:

Verification / Alternative check:Whether the digits can begin with 0 does not change the count; most telephone numbering schemes allow any 3-digit tail in this abstract setting.

Why Other Options Are Wrong:1/999, 1/990, 1/1001 are based on ad-hoc exclusions or inclusions that the problem statement does not impose.

Common Pitfalls:Assuming digits cannot be zero or must be distinct; no such constraints are given.

Final Answer:1/1000