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%)