Your regular tennis partner has offered a friendly wager to you. The two of you will play out one point in which you can serve. The loser pays the winner $100. If your first serve is not in play, you get a second serve. If your second serve is not in play, you lose the point.
You have two kinds of serves: a hard one and a soft one. You know that your hard serve is in play 65% of the time and, when it is in play, you win the point 75% of the time. You put your soft serve in play 88% of the time and, when it is in play, you win the point 27% of the time.
Construct a Decision Tree for this problem and answer the following questions:
1. Should you accept the wager?
2. What is the Expected Monetary Value?
3. If so, should you use your hard or soft serve?