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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 4.1.43c
Chapter 4, Problem 4.1.43c

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?

Verified step by step guidance
1
Step 1: Understand the problem. The question asks us to calculate the worth of a \$2 win ticket based on the payoff odds provided in part (c). Payoff odds represent the ratio of the net profit to the original bet amount.
Step 2: Recall the formula for calculating the total worth of a winning ticket: Total Worth = Original Bet + (Original Bet × Payoff Odds).
Step 3: Substitute the given values into the formula. The original bet is \$2, and the payoff odds are provided in part (c) (you would need to refer to the odds from part (c) to proceed).
Step 4: Perform the multiplication to calculate the net profit: Multiply the original bet (\$2) by the payoff odds to find the profit.
Step 5: Add the original bet amount (\$2) to the calculated profit to determine the total worth of the winning ticket.

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Key Concepts

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

Payoff Odds

Payoff odds represent the amount of money a bettor receives in return for a winning bet, relative to the amount wagered. In this case, the payoff odds for a $2 bet on Justify winning were $7.80, meaning the bettor receives $7.80 for every $2 wagered. Understanding payoff odds is crucial for calculating potential returns on bets.
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Betting Odds

Betting odds indicate the probability of a particular outcome occurring, often expressed in fractional or decimal form. They help bettors assess the risk and potential reward of their wagers. In the context of the Kentucky Derby, knowing the odds can inform decisions on how much to bet and which horses to back.
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Expected Value

Expected value is a statistical concept that calculates the average outcome of a bet if it were placed multiple times. It is determined by multiplying the probability of each outcome by its respective payoff and summing these products. Understanding expected value helps bettors make informed decisions by evaluating whether a bet is worth the risk based on potential returns.
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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

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?

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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

Corporate Officers and Committees The Self Driving Unicycle Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO), and chief human resources officer (CHR). It must also appoint a strategic planning committee with five different members. There are 15 qualified candidates, and officers can also serve on the committee.


b. How many different ways can a committee of five be appointed?


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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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