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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 4.1.3a
Chapter 4, Problem 4.1.3a

Dice and Coins


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

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Step 1: Understand the problem. We are tasked with finding the probability of rolling a 5 on a single six-sided die. A six-sided die has six equally likely outcomes: {1, 2, 3, 4, 5, 6}.
Step 2: Recall the formula for probability. The probability of an event occurring is given by: P(E)=Number of favorable outcomesTotal number of possible outcomes.
Step 3: Identify the favorable outcomes. In this case, the favorable outcome is rolling a 5, which is just one specific outcome.
Step 4: Identify the total number of possible outcomes. Since the die has six sides, there are 6 possible outcomes in total.
Step 5: Substitute the values into the probability formula. Using the formula from Step 2, substitute the number of favorable outcomes (1) and the total number of possible outcomes (6) to calculate the probability.

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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. An event with a probability of 0 means it cannot happen, while a probability of 1 means it is certain to happen. In the context of rolling a die, the probability of rolling a specific number is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
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Sample Space

The sample space is the set of all possible outcomes of a random experiment. For a single six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which favorable outcomes are compared.
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Favorable Outcomes

Favorable outcomes refer to the specific results of an experiment that satisfy the condition of interest. In the case of rolling a die and wanting to find the probability of rolling a 5, there is only one favorable outcome (rolling a 5) out of the six possible outcomes. This concept is essential for determining the probability by identifying how many outcomes meet the criteria of the event.
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Related Practice
Textbook Question

Phase I of a Clinical Trial A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.


a. If the subjects are selected and treated one at a time in sequence, how many different sequential arrangements are possible if 14 people are selected from the 16 that are available?


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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


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


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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

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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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

Redundancy in Computer Hard Drives The Seagate ST8000NM0055 hard drive has a 1.22% rate of failures in a year (based on data from Backblaze, Inc.). For the following, assume that all hard drives are that Seagate model.


a. If all of your computer data are stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? Express the result with six decimal places.

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