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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 4, Problem 4.4.6

Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. After seeing the last four digits printed on a receipt, if you randomly select the other digits, what is the probability of getting the correct Social Security number of the person who was given the receipt?

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Step 1: Understand the structure of a Social Security number. It consists of nine digits, and repetition of digits is allowed. Each digit can range from 0 to 9, giving 10 possible choices for each digit.
Step 2: Recognize that the last four digits are already known from the receipt. Therefore, you only need to randomly select the remaining five digits to match the correct Social Security number.
Step 3: Calculate the total number of possible combinations for the five unknown digits. Since each digit has 10 possible values and repetition is allowed, the total number of combinations is given by \( 10^5 \), which represents 10 choices for each of the 5 digits.
Step 4: Realize that there is only one correct combination of the five unknown digits that matches the Social Security number of the person who was given the receipt.
Step 5: Compute the probability of selecting the correct combination. The probability is the ratio of the number of favorable outcomes (1 correct combination) to the total number of possible outcomes (\( 10^5 \)). This can be expressed as \( P = \frac{1}{10^5} \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting the correct Social Security number from all possible combinations. Understanding how to calculate probability is essential for determining the likelihood of achieving a specific outcome.
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Combinatorics

Combinatorics is a branch of mathematics dealing with counting, arrangement, and combination of objects. In the case of Social Security numbers, it helps in calculating the total number of possible combinations of digits. Since there are nine digits with repetition allowed, combinatorial principles are crucial for understanding the total outcomes when selecting the digits.

Random Selection

Random selection refers to the process of choosing items from a set in such a way that each item has an equal chance of being chosen. In this scenario, it involves selecting the first five digits of a Social Security number randomly after knowing the last four. This concept is important for understanding how the selection process affects the probability of obtaining the correct number.
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