Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.4.24c

Chapter 4, Problem 4.4.24c

ATM You want to obtain cash by using an ATM, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.

c. How many random selections are required to be absolutely sure that the card works because it is inserted correctly?

Verified step by step guidance

Understand the problem: The card can be inserted into the ATM in four possible orientations. Only one of these orientations is correct, where the front side is up and the beginning of the name enters first.

List all possible orientations: (1) Front side up, name first (correct orientation), (2) Front side up, name last, (3) Back side up, name first, (4) Back side up, name last.

Recognize that to be absolutely sure the card works, you must test all four possible orientations, as there is no way to know in advance which one is correct.

Conclude that the number of random selections required to guarantee the correct orientation is equal to the total number of possible orientations, which is 4.

Verify the reasoning: Since there are 4 orientations and only one is correct, testing all 4 ensures that the correct orientation is eventually tested.

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Key Concepts

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

Random Selection

Random selection refers to the process of choosing items or options in such a way that each has an equal chance of being selected. In the context of the ATM card, it implies that you might need to try different orientations of the card to ensure it is inserted correctly. Understanding this concept is crucial for determining the number of attempts needed to guarantee success.

Permutations

Permutations are arrangements of objects in a specific order. For the ATM card, the orientation and order of insertion (front side up and name first) create different permutations. Knowing how to calculate permutations helps in understanding the total number of possible ways the card can be inserted, which is essential for determining how many attempts are necessary.

Probability

Probability is the measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this scenario, understanding the probability of successfully inserting the card correctly on the first try is important. This concept helps in assessing how many random selections might be needed to ensure that the card works, given the various possible orientations.

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Related Practice

Textbook Question

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)

Testing for Marijuana Use

c. What is the probability that a randomly selected subject had a true negative result?

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Textbook Question

Surge Protectors Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.

c. Which arrangement should be used for better protection?

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Textbook Question

Denomination Effect

In Exercises 13–16, use the data in the following table. In an experiment to study the effects of using four quarters versus a \$1 bill, some college students were given four quarters and others were given a \$1 bill, and they could either keep the money or spend it on gum. The results are summarized in the table (based on data from “The Denomination Effect,” by Priya Raghubir and Joydeep Srivastava, Journal of Consumer Research, Vol. 36).

Denomination Effect

b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.

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Textbook Question

Organ Donors USA Today provided information about a survey (conducted for Donate Life America) of 5100 adult Internet users. Of the respondents, 2346 said they are willing to donate organs after death. In this survey, 100 adults were surveyed in each state and the District of Columbia, and results were weighted to account for the different state population sizes.

b. Based on the poll results, what is the probability of randomly selecting an adult who is willing to donate organs after death?

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Textbook Question

Dice and Coins

c. Find the probability that when a six-sided die is rolled, the outcome is 7.

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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.

c. If the payoff odds were the actual odds found in part (c), what would be the worth of a \)2 win ticket after the Justify win?

194

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