Question 1197615
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Part (a)


Answer: <font color=red>$1.33</font>


Work Shown:
X = winnings<table border = "1" cellpadding = "5"><tr><td>X</td><td>P(X)</td><td>X*P(X)</td></tr><tr><td>150</td><td>1/150</td><td>1</td></tr><tr><td>10</td><td>5/150</td><td>1/3</td></tr><tr><td>0</td><td>144/150</td><td>0</td></tr></table>Add up the results in the X*P(X) column
E[X] = 1+1/3+0 = 4/3 = 1.33 approximately
The expected winnings is $1.33 approximately.
The player expects to win on average $1.33 per ticket (this is before the cost of the ticket is factored in).


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Part (b)


Answer: <font color=red>Profit</font>


Reason: 
The company expects to lose $1.33 per game when paying out the average winnings per ticket, as we found in part (a).
However, they gain $5 per ticket if they go for this ticket price.
The net profit per ticket from the company's perspective is -1.33+5 = 3.67
The company expects to gain $3.67 per ticket; while player expects to lose $3.67 per ticket.
These values represent averages.


If the ticket price was $1.33, then both sides neither win nor lose money. In such an event, we consider it a fair game. 
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