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
