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Chapter 16: Problem 66

Jackie is buying a new MP3 player from Better Buy. The store offers her a two- year extended warranty for \(\$ 19 .\) Jackie read in a consumer magazine that for this model MP3, \(5 \%\) require repairs within the first two years at an average cost of \$50. Should Jackie buy the extended warranty? Explain your reasoning.

Short Answer

Expert verified
No, Jackie should not buy the extended warranty. The expected cost if the warranty is not purchased (\$2.5) is lower than the cost of the warranty (\$19).

Step by step solution

01

Calculate the cost if warranty is purchased

If Jackie buys the extended warranty, the cost is given directly in the problem, which is \(\$19\).
02

Calculate the expected cost if warranty is not purchased

If Jackie does not buy the extended warranty, there is a \(5 \%\) chance that she will need to pay for repairs, at a cost of \(\$50\). To find the expected cost in this scenario, multiply the cost of repair by the probability of needing repair, which is \(\$50 * 0.05 = \$2.5\).
03

Compare the costs

Now, compare the cost in both scenarios. The cost if the warranty is purchased is \(\$19\), and the expected cost if the warranty is not purchased is \(\$2.5\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Expected Value
Expected value is a fundamental concept in decision-making, especially when dealing with uncertain outcomes. It allows individuals to calculate the average outcome when confronted with risk. In the context of Jackie's decision about purchasing an extended warranty for her MP3 player, expected value plays a crucial role. By understanding this concept, Jackie can make a more informed decision about whether the upfront cost of the warranty is worth the potential cost savings it might offer if something goes wrong.
  • Expected Value Formula: To compute the expected value, multiply each possible outcome by the probability of that outcome and then sum all these values.
  • Application: For Jackie's situation, the expected cost without the warranty is \\(50 * 0.05 = \\)2.5\, representing the average cost she would face for repairs.
Understanding expected value helps to evaluate risks and benefits, key to making wise consumer choices.
Consumer Decision Analysis
Consumer decision analysis is all about understanding and evaluating the costs and benefits associated with making purchasing decisions. When Jackie is considering whether to buy an extended warranty, she's engaging in a consumer decision analysis. This involves weighing the upfront cost of the warranty against the potential savings from avoiding repair costs. Decision-making strategies can include:
  • Assessing Risk: How likely is it that the MP3 player will need repairs?
  • Evaluating Cost: What is the cost difference between buying the warranty and facing potential repair costs?
  • Analyzing Reliability: Are there reviews or reports about the product鈥檚 reliability?
Jackie's decision involves analyzing these factors to make a choice that best suits her financial interests and peace of mind.
Mathematical Reasoning
Mathematical reasoning is at the heart of analyzing decisions such as whether to purchase a warranty. It involves applying logical steps and mathematical calculations to make sense of real-world problems. In Jackie's scenario, mathematical reasoning helps determine the expected costs and compare them with the actual cost of the warranty. This process involves:
  • Calculating Probabilities: Understanding percentage chances of failure.
  • Applying Formulas: Using the expected value formula to find potential repair costs.
  • Logical Comparisons: Evaluating different scenarios and their outcomes.
This kind of reasoning enables individuals like Jackie to make choices based on numerical evidence rather than just intuition or advertising.
Cost-Benefit Analysis
Cost-benefit analysis is a systematic approach to estimating the strengths and weaknesses of different options. Jackie can use this to determine whether the extended warranty is a good investment. This analysis involves:
  • Quantifying Costs: Both the initial warranty cost and potential repair costs.
  • Comparing Outcomes: The cost of the warranty versus the expected repair costs.
  • Decision Making: Concluding whether the warranty provides value based on the comparative analysis.
By conducting a cost-benefit analysis, consumers can make decisions that will offer them the greatest benefit for the lowest cost, which is what Jackie aims to do in her assessment of buying a warranty.

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Most popular questions from this chapter

A box contains twenty \(\$ 1\) bills, ten \(\$ 5\) bills, five \(\$ 10\) bills, four \(\$ 20\) bills, and one \(\$ 100\) bill. You blindly reach into the box and draw a bill at random. What is the expected value of your draw?

The board of directors of the XYZ Corporation has 15 members. (a) How many different slates of four officers (a President, a Vice President, a Treasurer, and a Secretary) can be chosen? (b) A four-person committee needs to be selected to conduct a search for a new CEO. In how many ways can the search committee be selected?

Andy and Roger are playing in a tennis match. (A tennis match is a best-of- five contest: The first player to win three games wins the match, and there are no ties.) We can describe the outcome of the tennis match by a string of letters \((A\) or \(R\) ) that indicate the winner of each game. For example, the string \(R A R R\) represents an outcome where Roger wins games \(1,3,\) and \(4,\) at which point the match is over (game 5 is not played). (a) Describe the event "Roger wins the match in game \(5 . "\) (b) Describe the event "Roger wins the match." (c) Describe the event "the match goes five games."

A basketball player shoots two consecutive free throws. Each free-throw is worth 1 point and has probability of success \(p=3 / 4\). Let \(X\) denote the number of points scored. Find the expected value of \(X\).

In head-to-head, 7 -card stud poker you make your hand by selecting your 5 best cards from the 2 in your hand and 3 from the 5 common cards showing on the table (the "flush draw") \(-\) if the last card ("river" card) is a spade you will have an ace high flush and a guaranteed win. Assume that your opponent has a decent hand and if you don't get the spade on the river card you will lose the hand. (a) Suppose there is \(\$ 100\) in the pot and your opponent moves "all-in" with a \(\$ 50\) bet. Should you call the bet or fold? Explain. (b) Suppose there is \(\$ 100\) in the pot and your opponent moves "all-in" with a \(\$ 20\) bet. Should you call the bet or fold? Explain.
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