Play now? Play later?
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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