Question 1050934
In Illinois Pick 3 game, you pay 50 cents to select a sequence 
of 3 digits, such as 285. (There are 1000 possible combinations.) 
If you win by selecting the correct sequence of digits, you 
collect $250.

a. Find the net profit for winning, and find the expected value.<pre>

The net profit if you win = $250.00-$0.50 = $249.50

 Events       Winnings     Probability     Expectation   
                 X             p(X)           X*P(X)
Selecting 
the right     $249.50         0.001          $0.2495
number

Selecting
the wrong      -$0.50         0.999         -$0.4995
number 
----------------------------------------------------
                        Total expectation = -$0.25
</pre>
b. What does this expected value mean?
<pre>
This means if you were to play this game thousands of 
times, sooner or later you will win.  But if you average 
up your winnings of +$250 and your losses -$0.50 over all
those times you played, you will find that you have averaged 
losing about a quarter every time you played.  

[The owner of the game is averaging profiting a quarter 
every time somebody plays.  In other words, the owner 
averages keeping half of all the money his (or her)
customers pay to play.] 

Edwin</pre>