Correction of Exercise 1, Chapter 3:

Correction of Exercise 1, Chapter 3:

1.     Roath is running clothes shop. She is also a teacher. Her shop opens from 8:00 am to 7:00 pm every day. She thinks if every weekend, she opens shop from 10 am, she will sell up to $250.00. If she starts at 2 pm, she will get about $ 150.00 per day, and if she start late at 4 pm and close at 8:00 pm, she will get only about $ 100.00 per day.

Please find out how much her average expected return per day ?

As mentioned, there are 3 events possible to occur.

So, the Formula Expected value – Ev = R1.P1  + R2.P2 + R3.P3

Where

R1 is return of event 1, open at 10 am: 250

R2 is return of event 2, open at 2 pm: 150

R3 is return of event 3, open at 4 pm: 100

As we know, Total PD = 1 = 100%

And P 1 + P2 + P3 = Total PD

And P1 + P2 + P3 = 100%
Suppose Total return from all events, R1 + R2 + R3 = 100%

Then we can get: Total PD = Total Return = 100%

Then we can get 250 + 150 + 100 = 100%

           500 = 100%

As the percentage of all three events.
P1 is percentage of return from Event1 (R1 = 250)

       If Total Return (500) = 100%

       Then R1 (250) = P1

ð  P1 = (250x100) / 500 = 50% = 0.5

P2 is percentage of return from Event2 (R2=150)

If Total Return (500) = 100%

       Then R2 (150) = P2

ð  P2 = (150x100) / 500 = 30% = 0.3

P3 is percentage of return from Event3 (R3=100)

If Total Return (500) = 100%

       Then R3 (100) = P3

ð  P3 = (100x100) / 500 = 20% = 0.2

Testing: P1+P2+P3 = 1

We get  0.5 + 0.3 + 0.2 = 1 (correct)

Then Ev = (250x0.5) + (150x0.3) + (100x0.2) = 190

Finally, his average expected return from her sale is Ev = $ 190