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 (and for a mere $2500 entry fee), then here are you chances:
0.10% that you receive $5,000,000, 45% that you break even and get back your entry fee, otherwise you receive nothing at all.
But wait, there's more! For only $3000 more, if (and only if) you don't win the 5 million on your first attempt then
you can choose to play one more time. If you do, then we dramatically increase your probability
of winning big - yes, you will hava a 4% chance of receiving $100,000 and 55% chance of winning $5000, but otherwise, you will have to pay an additional $10,000.
What is your expected outcome for attempting this venture? Solve this problem using
a decision tree and clearly show all calculations and the 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, should you try again? (5%) Why? (5%)
3) If you play and win your money back on the first try, should you try again? (5%) Why? (5%)
4) clearly show the decision tree (40%) and expected net monitary value at each node (25%)