Data Mining

You   can become a millionaire! That’s what   the junk mail said. But then there was   the fine print:

 

If   you send in your entry before midnight tonight, then here are your chances:

 

0.1%   that you win $1,000,000

 

75%   that you win nothing

 

Otherwise,   you must PAY $1,000

 

But   wait, there’s more! If you don’t win   the million AND you don’t have to pay on your first attempt,

 

then   you can choose to play one more time. If you choose to play again, then here are your chances:

 

2% that   you win $100,000

 

20%   that you win $500

 

Otherwise,   you must PAY $2,000

 

 

What   is your expected outcome for attempting this venture? Solve this problem using

 

a   decision tree and clearly show all calculations and the expected monetary   value at each node.

 

Use   maximization of expected value as your decision criterion.

 

Answer   these questions:

 

1)   Should you play at all? (5%) If you   play, what is your expected (net) monetary value? (15%)

 

2) If   you play and don’t win at all on the first try (but don’t lose money), should   you try again? (5%) Why? (10%)

 

3)   Clearly show the decision tree (40%) and expected net monetary value at each   node (25%)

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