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.
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
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Total expectation = -$0.25
b. What does this expected value mean?
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