A company estimates that 0.4% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $50.
If they offer a 2 year extended warranty for $3, what is the company's expected value of each warranty sold?
To calculate the company's expected value of each warranty sold, we need to consider the potential outcomes and their associated probabilities.
The probability of a product failing after the original warranty but within 2 years of purchase is given as 0.4%, or 0.004. Let's denote this event as "Failure". The replacement cost for each failed product is $50.
Now, let's consider the two possible scenarios:
1. The product fails after the original warranty period but within 2 years of purchase (Event: Failure)
- Probability of this event: 0.4% or 0.004
- Replacement cost: $50
2. The product does not fail after the original warranty period and remains functional (Event: Not Failure)
- Probability of this event: 100% - 0.4% = 99.6% or 0.996
- Replacement cost: $0
To calculate the expected value, we multiply each outcome by its respective probability and sum them up:
Expected value = (Probability of Failure * Replacement cost) + (Probability of Not Failure * Replacement cost)
= (0.004 * $50) + (0.996 * $0)
= $0.2 + $0
= $0.2
Therefore, the company's expected value of each warranty sold is $0.2.