Suppose Best Buy offers an extended warranty for $25 on an electronic device whose value is $200. Suppose Best Buy estimates the probability the item will be returned for a claim on that warranty is 10%. Assume that if the item is returned, Best Buy will refund the $200 purchase price. What is Best Buy’s expected value on the warranty?
Lets see what is given:
Best Buy is the seller of electronic device. The Best Buy sell an electronic device for $200. And Extended Warranty is for $25.
That’s the Best Buy company get $25 for the warranty.
The probability of the item return is 10% or 0.10.
So, the probability of item that won’t return is 100%-10%= 90% or 0.90.
Let’s see what it asks to find:
It asked to find the Best Buy’s expected value on Warranty.
We Know expected value is E(x)= P(x1)*x1 +P(x2)*x2+….
Here according to the Best Buy’s view we can make the table of value and it’s probability.
Value 25 -200 0
Probability 1 0.1 0.90
Here, 25 is the income with probability 1 of Best buy whether it return back or non return back the electronic item. Because customer has to pay for the warranty.
Now, for value 200(When it returns back to Best Buy company) the probability is 0.1.
When it is not return back we do consider it’s value is 0, with probability 0.9
Now, using Expected value formula
E(x) = 25-20+0
So, Expected value for Best Buy is $5.
I hope it make sense!:)