Question 1200362
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Answer = <font color=red size=4>-13.28</font>


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Explanation:


X = net winnings


If a person wins $1300, and the ticket costs $15, then they walk away with $1285 (since 1300-15 = 1285)
In short: X = 1285 is one possibility.


The other outcome is when X = -15 to represent cases when the person doesn't win anything. Even worse: They lost $15.


There's 1 winning ticket out of 758 total
1/758 represents the probability of winning, so it's tied to X = 1285
In other words, P(X) = 1/758 when X = 1285


1-(1/758) = 757/758 is the probability connected to X = -15


To summarize so far<ul><li>P(X) = 1/758 when X = 1285</li><li>P(X) = 757/758 when X = -15</li></ul>Often it's handy to organize this information into a table 
<table border = "1" cellpadding = "5"><tr><td>X</td><td>P(X)</td></tr><tr><td>1285</td><td>1/758</td></tr><tr><td>-15</td><td>757/758</td></tr></table>
Use of spreadsheet software is strongly recommended. 


We'll then form a new column labeled X*P(X)
This is where we multiply each X with its corresponding P(X) value
<table border = "1" cellpadding = "5"><tr><td>X</td><td>P(X)</td><td>X*P(X)</td></tr><tr><td>1285</td><td>1/758</td><td>1285/758</td></tr><tr><td>-15</td><td>757/758</td><td>-11355/758</td></tr></table>
Then we add up the results of that new column.
(1285/758)+(-11355/758)
(1285-11355)/758
-10070/758
-13.2849604221636
<font color=red>-13.28</font>


That is the approximate expected value. More specifically, it's the approximate expected net winnings.
It means that the average person expects to lose about $13.28


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Another approach:


The previous method used the standard textbook approach with expected value problems. That template outline being: <ol><li>Construct the probability distribution table of each X and P(X)</li><li>Compute X*P(X) for each row.</li><li>Add up each X*P(X) value</li></ol>For this second approach, imagine a single person buying all 758 tickets at $15 each.
In total, they spent 758*15 = 11370 dollars.


That means they are down this amount. 
We write -11370 to indicate this loss.


But this player is guaranteed to win the prize of $1300 because they bought all the tickets.
Their net winnings is -11370+1300 = -10070
They're still down a considerable amount of money.


Divide this net loss over the number of tickets to determine the average loss per ticket.
-10070/758 = -13.2849604221636 = <font color=red>-13.28</font>


Therefore, this player lost on average approximately $13.28 per ticket.


Hopefully you notice that these calculations are very similar to the previous section's calculations. 
The numbers haven't changed too much. 
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