Probability word problem

Question

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 $400.

If they offer a 2-year extended warranty for $22. Complete the probability distribution table. Let x be the profit (which could be negative in the case of a loss). List the x values from smallest to largest. Remember to list the P(x) as a probability, not a percent. This problem is from the company's point of

Answer 1

Mac, thanks for bringing up one of my favorite type of stat problems!

Given Data:

1. Probability of product failure: 0.4% or 0.004
2. Replacement cost: $400
3. Cost of 2-year extended warranty: $22

Objective: Create a probability distribution table for profit (x).

Scenarios:

1. Product Fails
2. Profit: $22 - $400 = -$378
3. Probability: 0.004
4. Product Does Not Fail
5. Profit: $22
6. Probability: 0.996

Probability Distribution Table

Profit (x)Probability (P(x))
-378	0.004
22	0.996

Further Exploration:

1. Expected Profit: The expected profit can be calculated as the weighted average of all possible profits.

�(�)=−378×0.004+22×0.996E(x)=−378×0.004+22×0.996

1. Risk Assessment: The company stands a very low risk of making a loss on the extended warranty, as indicated by the high probability (0.996) of making a $22 profit.
2. Pricing Strategy: The company could potentially increase the price of the extended warranty if it wants to hedge against other operational costs or increase profit margins. However, this could affect customer perception and demand.
3. Customer Behavior: This analysis assumes that all customers who purchase the product also opt for the extended warranty, which might not be the case in reality. If fewer people opt in, the risk could be different.
4. Cost Variability: The replacement cost is assumed to be a constant $400. Any variability in this cost would add complexity to the model.

If you found this helpful, I would greatly appreciate your feedback! Reviews are super helpful for me since I am new to the platform (though very experienced in stats!).

Thank you,

Ben