Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random.

a. What is the probability of randomly generating 16 digits and getting your MasterCard number?

검증된 단계별 안내

Understand the problem: The goal is to calculate the probability of randomly generating a specific 16-digit MasterCard number. This involves understanding the total number of possible 16-digit combinations and recognizing that only one specific combination matches your MasterCard number.

Determine the total number of possible 16-digit combinations: Since each digit can range from 0 to 9, there are 10 possible choices for each digit. For 16 digits, the total number of combinations is calculated as \( 10^{16} \).

Recognize the favorable outcome: There is only one specific 16-digit number that matches your MasterCard number. This means there is exactly one favorable outcome out of the total possible outcomes.

Calculate the probability: The probability of randomly generating your specific MasterCard number is the ratio of favorable outcomes to total outcomes. This can be expressed as \( \frac{1}{10^{16}} \).

Interpret the result: The probability is extremely small because \( 10^{16} \) is a very large number, making it highly unlikely to randomly generate your specific MasterCard number.

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주요 개념

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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 generating a specific 16-digit number, such as a MasterCard number, from all possible combinations of 16 digits.

Random Number Generation

Random number generation involves creating a sequence of numbers that lack any predictable pattern. For credit card numbers, each digit can range from 0 to 9, leading to a total of 10 possible choices for each of the 16 digits, which is crucial for calculating the total number of possible combinations.

Combinatorial Analysis

Combinatorial analysis is a branch of mathematics dealing with counting, arrangement, and combination of objects. In this scenario, it helps determine the total number of unique 16-digit combinations possible, which is essential for calculating the probability of randomly generating a specific credit card number.

Identity Theft with Credit Cards Credit card numbers typically have 16 digits, but not all of them are random.a. What is the probability of randomly generating 16 digits and getting your MasterCard number?