Question

4. I want to open a bakery and I am considering locations at two different shopping centers. Use expected value to determine which location I should use.
Location 1: Location 2:
According to my consultant, if the bakery is successful, I can anticipate an annual profit of $300,000. If it’s not successful, I can anticipate an annual loss of $100,000. The probability of success of this location is 0.5.
According to my consultant, if the bakery is successful, I can anticipate an annual profit of $200,000. It it’s not successful, I can anticipate an annual loss of $60,000. The probability of success at this location is 0.75.

Answer 1

For location 1:
Probability of success = 0.5
Probability of failure  = 1 - Probability of success = 0.5

Expected Value for Location 1 will be:
$E(1)=0.5(300000)-0.5(100000)= 100000$

For location 2:
Probability of success = 0.75
Probability of failure = 1 - 0.75 = 0.25
So, expected value for Location 2 will be:
$E(2)=0.75(200000)-0.25(60000)= 135000$

The expected value from Location 2 is larger than Location 1, so Location 2 must be used to open up a bakery.