Question 1201591
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Part (a)


C = card value = 1,2,3,...,9,10
W = winnings in dollars


If C is odd, then W = -7 to indicate he lost $7.
If C is even, then W = C  (eg: C = 8 means Trey won $8)
Each P(W) value is 1/10 = 0.1 assuming each card is likely to be chosen.


Here is one way to write out the probability distribution.
<table border = "1" cellpadding = "5"><tr><td>C</td><td>W</td><td>P(W)</td></tr><tr><td>1</td><td>-7</td><td>0.1</td></tr><tr><td>2</td><td>2</td><td>0.1</td></tr><tr><td>3</td><td>-7</td><td>0.1</td></tr><tr><td>4</td><td>4</td><td>0.1</td></tr><tr><td>5</td><td>-7</td><td>0.1</td></tr><tr><td>6</td><td>6</td><td>0.1</td></tr><tr><td>7</td><td>-7</td><td>0.1</td></tr><tr><td>8</td><td>8</td><td>0.1</td></tr><tr><td>9</td><td>-7</td><td>0.1</td></tr><tr><td>10</td><td>10</td><td>0.1</td></tr></table>
Feel free to replace each 0.1 with 1/10 if you prefer.


Or we could condense things like so
<table border = "1" cellpadding = "5"><tr><td>C</td><td>W</td><td>P(W)</td></tr><tr><td>2</td><td>2</td><td>0.1</td></tr><tr><td>4</td><td>4</td><td>0.1</td></tr><tr><td>6</td><td>6</td><td>0.1</td></tr><tr><td>8</td><td>8</td><td>0.1</td></tr><tr><td>10</td><td>10</td><td>0.1</td></tr><tr><td>odd number</td><td>-7</td><td>0.5</td></tr></table>


Multiply each W and P(W) value to form a new column.


<table border = "1" cellpadding = "5"><tr><td>C</td><td>W</td><td>P(W)</td><td>W*P(W)</td></tr><tr><td>2</td><td>2</td><td>0.1</td><td>0.2</td></tr><tr><td>4</td><td>4</td><td>0.1</td><td>0.4</td></tr><tr><td>6</td><td>6</td><td>0.1</td><td>0.6</td></tr><tr><td>8</td><td>8</td><td>0.1</td><td>0.8</td></tr><tr><td>10</td><td>10</td><td>0.1</td><td>1</td></tr><tr><td>odd number</td><td>-7</td><td>0.5</td><td>-3.5</td></tr></table>
Then add up the results of that new column.
0.2+0.4+0.6+0.8+1+(-3.5) = -0.5


This is the expected value.
The average amount Trey expects to lose on any given game is $0.50 aka 50 cents.


Answer: <font color=red>-0.50</font>


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Part (b)


Let's say he plays this game 1000 times.
This would mean he expects to lose  0.50*1000 = 500 dollars over the course of those 1000 games.
He might get lucky to win money once in a while, but the long run odds are stacked against him. 


In general, if he plays n games, then he'll expect to lose 0.50n dollars on average.
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