SOLUTION: Party Time Co. will run a promotional raffle that offers a chance to win either a lifetime discount on Spring Festival Merchandises (which results in a $1,000 savings) or a 5-year

Question 579176: Party Time Co. will run a promotional raffle that offers a chance to win either a lifetime discount on Spring Festival Merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $400 savings).
a) Winning a lifetime discount has a 1-in-100 chance.
b) Winning a 5-year limited discount has a 1-in-20 chance.
Is this promotion worth it if the tickets cost $35?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Party Time Co. will run a promotional raffle that offers a chance to win either a lifetime discount on Spring Festival Merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $400 savings).
a) Winning a lifetime discount has a 1-in-100 chance.
b) Winning a 5-year limited discount has a 1-in-20 chance.
Is this promotion worth it if the tickets cost $35?
-----
Random winning values:::::::::: 965::::::: 365 ::::::: -35
Corresponding probabilities:::: 1/100 :::::5/100::::: 94/100
---------------
Expected Value = (965 + 5*365 - 94*35)/100 = -1230/100 = -$12.30
----
The company will gain $12.50 on each ticket that is bought.
The ticket buyer can expect to lose $12.50 on each ticket bought.
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Cheers,
Stan H.

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