A consumer is buying a new smartphone and is offered a one-year warranty for $150. Based on historical data, there is a 10% chance the phone will require a major repair during that year, which would cost $800. A calculation shows that the expected cost of repairs without the warranty is $80. Despite this, the consumer decides to purchase the $150 warranty. Which statement best evaluates this consumer's decision?
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Laptop Warranty Decision
You are considering a one-year extended warranty for a new appliance that costs $100. There is a 20% probability that the appliance will need a major repair during the year, which would cost $600. If it does not break, the repair cost is $0. Based solely on minimizing expected costs, what is the most financially rational decision?
Warranty Decision Break-Even Point
An individual purchases a one-year, $150 warranty for a new television. They estimate there is a 30% chance the television will require a repair that would cost $600 without the warranty. At the end of the year, the television has not needed any repairs. The individual concludes that buying the warranty was a poor financial decision because they 'wasted' $150. Which statement best evaluates this conclusion from a probabilistic decision-making perspective?
A person is considering whether to purchase a $75 extended warranty for a new electronic device. They have determined that if the device fails, the cost to repair it will be $400. To make a financially rational decision based on expected outcomes, what is the most critical piece of information they still need?
A consumer is buying a new tablet and is presented with two warranty options. The tablet has a 20% chance of needing a repair within the warranty period, which would cost $400.
- Plan A: A one-time fee of $90 that covers the full cost of any repair.
- Plan B: A one-time fee of $50, plus a $100 deductible that must be paid only if a repair is needed.
Based on a purely financial calculation of expected costs, which of the following is the most rational choice?
Multi-Failure Scenario Warranty Decision
A consumer is buying a new smartphone and is offered a one-year warranty for $150. Based on historical data, there is a 10% chance the phone will require a major repair during that year, which would cost $800. A calculation shows that the expected cost of repairs without the warranty is $80. Despite this, the consumer decides to purchase the $150 warranty. Which statement best evaluates this consumer's decision?
A consumer is deciding whether to buy a $50 one-year warranty for a new coffee machine. They estimate there is a 15% chance the machine will break, requiring a $200 repair. Based on these numbers, the expected cost of going without the warranty is $30 (0.15 * $200), which is less than the $50 warranty price, so they initially decide against it. Which of the following new pieces of information would be most likely to make purchasing the warranty the more financially sound decision?
A consumer is deciding whether to buy a $150 warranty for a new drone. They estimate a 40% probability of a crash that would require a $500 repair. The consumer reasons as follows: 'My expected loss from a crash is $200 (0.40 * $500), but my expected gain from not crashing is $300 (0.60 * $500). Since the expected gain is higher than the expected loss, I will not buy the warranty.' What is the primary error in this line of reasoning?