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Ch. 4 - Probability
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 4 - ProbabilityProblem 4.4.26a
Chapter 4, Problem 4.4.26a

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?

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1
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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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 generating a specific 16-digit number, such as a MasterCard number, from all possible combinations of 16 digits.
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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.
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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.
Related Practice
Textbook Question

Alarm Clock Life Hack Each of us must sometimes wake up early for something really important, such as a final exam, job interview, or an early flight. (Professional golfer Jim Furyk was disqualified from a tournament when his cellphone lost power and he overslept.) Assume that a battery-powered alarm clock has a 0.005 probability of failure, a smartphone alarm clock has a 0.052 probability of failure, and an electric alarm clock has a 0.001 probability of failure.

a. What is the probability that your single battery-powered alarm clock works successfully when you need it?

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Textbook Question

Kentucky Derby Odds When the horse Justify won the 144th Kentucky Derby, a \$2 bet on a Justify win resulted in a winning ticket worth \(7.80.


a. How much net profit was made from a \)2 win bet on Justify?

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Textbook Question

Is the Researcher Cheating? You become suspicious when a genetics researcher “randomly” selects numerous groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher claims that it is common to get 10 girls and 10 boys in such cases.


a. If 20 newborn babies are randomly selected, how many different gender sequences are possible?


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Textbook Question

Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number.


a. What is your probability of winning?

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Textbook Question

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting and Alcohol If three of the high school drivers are randomly selected from the 4720 subjects who did not text while driving, find the probability that all three drove when drinking.


a. Assume that the selections are made with replacement. Are the events independent?

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Textbook Question

Dice and Coins


a. Find the probability that when a single six-sided die is rolled, the outcome is 5.

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