Question 1206326
<font color=black size=3>
Answer: <font color=red size=4>-1.31 dollars</font>
It means you should expect to lose about $1.31 per ticket.


Explanation


Let's say you really wanted to win.
To fully guarantee a win, you'd have to buy all 15,000 tickets.
That would cost you 15000*2 = 30,000 dollars.
Buying all of the tickets would bring in 1*8600+2*660+4*56+10*20 = 10,344 dollars.


total cost = $30,000
winnings = $10,344


net = winnings - cost
net = $10,344 - $30,000
net = -19656 dollars
The negative amount means you'd lose money.


Divide that net amount over the total number of tickets.
-19656/15000 = -1.3104
You should expect to lose, on average, about $1.31 per ticket.


<s>Tutor ikleyn has the right idea but made a slight typo.
The 600 should be 660.</s>
Edit: The situation has been fixed. 


--------------------------------------------------------------------------


Another approach.
This is probably the more standard approach to expected value problems.


x = net winnings (after factoring in the cost of the ticket)
Example: x = 8600-2 = 8598 if you won the grand prize
<table border = "1" cellpadding = "5"><tr><td>x</td><td>P(x)</td><td>x*P(x)</td></tr><tr><td>8598</td><td>0.000067</td><td>0.576066</td></tr><tr><td>658</td><td>0.000133</td><td>0.087514</td></tr><tr><td>54</td><td>0.000267</td><td>0.014418</td></tr><tr><td>18</td><td>0.000667</td><td>0.012006</td></tr><tr><td>-2</td><td>0.998867</td><td>-1.997734</td></tr><tr><td></td><td>Sum</td><td>-1.30773</td></tr></table>
Each decimal value is approximate to 6 decimal places.
1/15000 = 0.000067
2/15000 = 0.000133
4/15000 = 0.000267
10/15000 = 0.000667
14983/15000 = 0.998867



Spreadsheet software is strongly recommended. I used LibreOffice.
Add up the items in the x*P(x) column to get roughly -1.30773
There's some rounding error since the result should be exactly -1.3104


If we increase the rounding precision, say to 8 decimal places, then this is what the table would look like
<table border = "1" cellpadding = "5"><tr><td>x</td><td>P(x)</td><td>x*P(x)</td></tr><tr><td>8598</td><td>0.00006667</td><td>0.57322866</td></tr><tr><td>658</td><td>0.00013333</td><td>0.08773114</td></tr><tr><td>54</td><td>0.00026667</td><td>0.01440018</td></tr><tr><td>18</td><td>0.00066667</td><td>0.01200006</td></tr><tr><td>-2</td><td>0.99886667</td><td>-1.99773334</td></tr><tr><td></td><td>Sum</td><td>-1.3103733</td></tr></table>
The result -1.3103733 is a bit more closer to -1.3104
Either way both results round to -1.31 dollars when rounding to the nearest cent.
</font>