Question 211653
500 tickets for prizes are sold for $2 each. Five prizes will be awarded- one for $300, one for $200, and three for $50. Steven purchases one of the tickets. 
a) Find the expected value
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His possible net winnings are 

gain
 or
loss    probability
---------------------      
$298    1/500 = .002
$198    1/500 = .002
 $48    3/500 = .006
 -$2  495/500 = .990


{{{Expectation=298*(1/500)+198(1/500)+48(3/500)+(-2)(495/500)=-.70}}}

So he would average losing 70 cents if the same lottery were
held many times and he bought one ticket each time. 

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b) Find the fair price of the ticket.
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This equals the value of the ticket if the ticket were free.

If the ticket were free you could not lose money.  Then
the lottery would be like this:

gain
 or
loss  probability
      
$300    .002
$200    .002 
 $50    .006

{{{Expectation=(300)(.002)+(200)(.002)+(50)(.006)=1.30}}}

So a fair price for the ticket would be $1.30

Edwin</pre>