Question 1186121
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Tickets for a raffle cost $12. There were 713 tickets sold. One ticket will be randomly selected 
as the winner, and that person wins $1800 and also the person is given back the cost of the ticket. 
For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
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I do not agree with the solution in the post by @CPhill.


<pre>
    He calculates the net winning of the winner as


        Net winnings = $1800 + $12 = $1812.


    @CPhill adds $12 to the winning, but forgets to subtract $12 for buying the ticket.

    The correct way to calculate and the correct value of the net winning is, of course,

        - $12 + $1800 + $12 = $1800.


    Accordingly, all other numbers in the solution should be changed.
</pre>


After that explanation, see my correct solution below.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>S O L U T I O N</U>



<pre>
Here's how to calculate the expected value of a raffle ticket:

**1. Calculate the probability of winning:**

* There is 1 winning ticket out of 713 total tickets.
* Probability of winning = 1/713

**2. Calculate the net winnings if you win:**

* You spent @12 to buy a ticket, win $1800, and you get your $12 ticket cost back.   <<<---=== my corrections start from this point
* Net winnings = - $12 + $1800 + $12 = $1800

**3. Calculate the net loss if you lose:**

* You lose the cost of the ticket.
* Net loss = -$12

**4. Calculate the expected value:**

Expected Value = (Probability of Winning * Net Winnings) + (Probability of Losing * Net Loss)

Expected Value = (1/713 * $1800) + (712/713 * (-$12))

Expected Value ≈ -$-9.458625526     <<<---===  notice the difference with the value by -$9.42 in the solution by @CPhill

                                    <<<---===  also notice that I do not round it to cents, since this value is the statistical quantity

**Therefore, the expected value of the raffle ticket is approximately -$9.46.** This means that on average, a person buying a ticket can expect to lose about $9.46.
</pre>

Solved correctly.


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The difference may seem not to be significant, but in this problem not the magnitude of the difference
plays a role, but the correctness of the approach, developing right logic and the correctness of steps.


For the solution by @CPhill, strict examiner would give a solid &nbsp;&nbsp;{{{highlight(highlight(2))}}} &nbsp;&nbsp;and would send him for retraining.