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 4.2.26a

Chapter 4, Problem 4.2.26a

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?

Verified step by step guidance

Step 1: Understand the problem. The probability of failure for the battery-powered alarm clock is given as 0.005. To find the probability of success, we need to calculate the complement of the failure probability.

Step 2: Recall the complement rule in probability. The complement rule states that the probability of an event not occurring (failure) plus the probability of the event occurring (success) equals 1. Mathematically, this is expressed as: P(Success) = 1 - P(Failure).

Step 3: Substitute the given probability of failure into the complement formula. Here, P(Failure) = 0.005, so the formula becomes: P(Success) = 1 - 0.005.

Step 4: Perform the subtraction to find the probability of success. This step involves subtracting the failure probability from 1.

Step 5: Interpret the result. The calculated probability represents the likelihood that the battery-powered alarm clock will work successfully when needed.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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. A probability of 0 indicates that the event will not happen, while a probability of 1 indicates certainty. In this context, the probabilities given for each type of alarm clock represent the chance of failure, which can be used to calculate the chance of success.

Complementary Events

Complementary events are pairs of outcomes where one event occurs if and only if the other does not. For example, if the probability of an alarm clock failing is 0.005, the probability of it working successfully is the complement, calculated as 1 minus the failure probability. Understanding complementary events is crucial for determining the likelihood of success in scenarios involving failure rates.

Independent Events

Independent events are those whose outcomes do not affect each other. In the context of alarm clocks, if you consider multiple clocks, the failure of one does not influence the others. This concept is important when calculating the overall probability of success or failure when using multiple devices, as it allows for straightforward multiplication of individual probabilities.

Recommended video:

05:54

Probability of Multiple Independent Events

Related Practice

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.

119

views

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?

155

views

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?

160

views

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?

154

views

Textbook Question

Dice and Coins

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

301

views

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.

160

views