We will return to Bill and his barbershop. Bill is not going to open 100 barbershops. He is going to open only one barbershop, and there is obviously some chance that he will lose money each year. He cannot justify his investment by saying that the expectation was in his favor. Carlos and John could also wind up losing money.


Why We Need the Expectation

The answer is simple. The expectation gives us an estimate of the chances of success and failure. Were Bill to open 100 barbershops, or 1,000 barbershops, and were the profit on each one to exactly match our guidelines for the chances of making a profit or loss, the average profit per barbershop would be equal to the expectation.  

The higher the expected profit, the more willing Bill will be to open a barbershop. When the expectation is negative, it is more probable that Bill’s barbershop will lose money.

 We will analyze two scenarios for opening a barbershop, and compare their expectations:

  • Scenario 1 – opening a barbershop in Boston.  The data for this scenario are displayed in column     no. 1 and 2 of Table 3.12.
  • Scenario 2 – opening a barbershop in New York.  The data for this scenario are displayed in column no. 1 and 2 of Table 3.13.

The expected profit (or average profit) is calculated in each of the tables in the bottom row of column no. 3.  

Table 3.12

Scenario 1 – Boston
Amount of Annual Profit (Loss) Chance Contribution to Expectation
(1) (2) (3) = (1) X (2)
$100k 80% $80k
$70k 10% $7k
$–10k 10% $–1k
Expectation $86k

Table 3.13

Scenario 2 – New York
Amount of Annual Profit (Loss) Chance Contribution to Expectation
(1) (2) (3) = (1) X (2)
$100k 10% $10k
$70k 10% $7k
$–10k 80% $–8k
Expectation $9k


The expected profit in Boston is $86k, which is higher than the $9k expected profit in New York. It is therefore preferable to open  a barbershop in Boston.