This problem is from khan academy:
John just bought a brand new cell phone and is considering buying a warranty. The warranty costs 200 euros and is worth 1000 euros if his phone breaks. John estimates that there is a 10%, percent chance of his phone breaking.
Find the expected value of buying the warranty.
Step by step guide to the solution
Now, the reason why I created this question is because I am unsure of what the conclusion is. I assume that since the expected value is -100 euros, it means that we can expect to lose 100 euros by buying this warrenty; thus, we should not buy the warrenty.
- Is my assumption (conclusion) correct?
expected value function, where x = the probability of braking phone
- Would it be correct to assume that:
if the probability of the phone braking is over 20%, we should buy a warrenty, and simiarily avoid buying one if the probability is less than 20%.
The expected overall value of the warranty, as calculated, is -100 Euros.
On the other hand, assuming that without the warranty John will still purchase a new phone if his current one breaks, then there is a 90% chance John will pay nothing and a 10% chance he will have to pay 1000 Euros, making the expected value of not buying the warranty also -100 Euros.
In this case, as it turns out, there is no change in the value between buying and not buying the warranty so based on these calculations it doesn't matter if he does or not. However, if John valued certain outcomes differently (e.g. he doesn't want to have to pay large chunks of money, or he hates filling out forms), then you would need to used a different measure of the expected utility of the two options.