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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 4.1.43a
Chapter 4, Problem 4.1.43a

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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1
Identify the total payout from the winning ticket, which is \$7.80, and the initial bet amount, which is \$2.
Understand that the net profit is calculated by subtracting the initial bet amount from the total payout.
Write the formula for net profit: Net Profit = Total Payout - Initial Bet.
Substitute the given values into the formula: Net Profit = \(7.80 - \)2.
Simplify the expression to find the net profit, which represents the amount earned beyond the initial bet.

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Key Concepts

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

Net Profit

Net profit is the amount of money gained after subtracting the initial investment from the total returns. In betting, it is calculated by taking the winnings and deducting the amount wagered. For example, if a bettor wins $7.80 from a $2 bet, the net profit would be $7.80 - $2 = $5.80.
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Betting Odds

Betting odds represent the likelihood of a particular outcome occurring and determine how much a bettor can win. In this case, the odds for Justify winning were such that a $2 bet returned $7.80, indicating a favorable outcome. Understanding odds helps bettors assess potential returns and risks associated with their wagers.
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Return on Investment (ROI)

Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment. It is calculated by dividing the net profit by the initial investment and multiplying by 100 to get a percentage. In this scenario, the ROI from the $2 bet on Justify can help bettors understand the profitability of their wager relative to the amount they risked.
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?

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?


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


a. How many subjects are included in the study?

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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?


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?

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?