Question

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 1

To find the expected outcome of the game mentioned, one would create a decision tree, calculate the expected value at each chance node, and then add these values to determine the overall expected value of the game. The decision to play would be based on whether the expected value is positive or negative.

Step-by-step explanation:

Expected Outcome Calculation Using a Decision Tree

The expected value (EV) at each node of a decision tree represents the long-term average profit or loss if the game were played a very large number of times.Expected value is calculated by multiplying each possible outcome by its probability, and then summing the results.

The decision tree for the game described consists of a series of choices and chance events. The first decision is to send in the entry, which leads to a chance event with 0.1% probability of winning $1,000,000 and 75% of winning nothing. Should the player win nothing, there is an additional chance to play, which has its own probabilities of winning or losing money.

To solve for the expected outcome:

1. 
   
3. Calculate EV for each chance node.
4. 
   
6. Calculate the overall EV based on the possible pathways through the game.

Since this is a hypothetical question, the particular numbers (such as those for winning and payment amounts) would need to be provided in the question itself for a complete answer to be formulated. Given these numbers, one would perform the necessary calculations of EV and sum them to find the expected outcome. If the EV is positive, it implies that over the long term, one can expect to come out ahead financially. Otherwise, if the EV is negative, one can expect to lose money over the long term.