SOLUTION: HELP! losing my mind over this one. 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

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Question 211653: HELP! losing my mind over this one.
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
b) Find the fair price of the ticket.

Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
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

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




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

-----------------------

b) Find the fair price of the ticket.

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



So a fair price for the ticket would be $1.30

Edwin


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