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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 act
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 act before midnight tonight, then here are you chances: 0.1% that you receive $1,000,000; | ||||||||||
75% that you get nothing, otherwise you must PAY $5000. | ||||||||||
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 do, then we 20X your probability of winning big - yes, you will hava a 2% chance of | ||||||||||
receiving $100,000 and 60% chance of winning $7500, but must pay $10,000 otherwise. | ||||||||||
What is your expected outcome for attempting this venture? Solve this problem using | ||||||||||
a decision tree and clearly show all calculations and the expected value at each node. | ||||||||||
Answer these questions: | ||||||||||
1) should you play at all? (5%) And if so, what is my expected (net) monitary value? (10%) | ||||||||||
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? (5%) | ||||||||||
3) clearly show the decision tree (40%) and expected net monitary value at each node (25%) |
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