Social Security Numbers
A Social Security number is used to identify each resident of the United States uniquely. The number is of the form xxx-xx-xxxx, where each x is a digit from 0 to 9.
b. What is the probability of correctly guessing the Social Security number of the president of the United States?

Verified step by step guidance

1. Understand the structure of a Social Security number (SSN). It consists of 9 digits arranged in the format xxx-xx-xxxx, where each 'x' is a digit from 0 to 9.
2. Calculate the total number of possible SSNs. Since each digit can be any of 10 values (0 through 9), the total number of unique SSNs is \$10^9$.
3. Recognize that guessing the correct SSN is a single event out of all possible SSNs, so the probability of guessing correctly is the ratio of favorable outcomes (1 correct SSN) to total possible outcomes (\$10^9$).
4. Express the probability mathematically as \(\frac{1}{10^9}\).
5. Interpret this probability as an extremely small chance, reflecting how unlikely it is to guess the correct SSN by random chance.

Key Concepts

Sample Space and Counting Principles

The sample space represents all possible outcomes in a probability scenario. For Social Security numbers, each digit can be from 0 to 9, so the total number of possible SSNs is calculated using counting principles, specifically multiplication of choices for each digit.

Probability of a Single Event

Probability measures the likelihood of a specific event occurring, calculated as the ratio of favorable outcomes to total possible outcomes. Here, guessing the exact SSN is one favorable outcome out of all possible SSNs.

Uniform Probability Distribution

Assuming each Social Security number is equally likely, the probability distribution is uniform. This means every SSN has the same chance of being chosen or guessed, simplifying the calculation of the probability of guessing the correct number.