To Run or Not to Run: You're a sprinter, and in practice today you fell and hurt your leg. An x-ray suggests that it's broken with probability 0.2. Your problem is deciding whether you should participate in next week's tournament. If you run, you think you'll win with probability 0.1. If your leg is broken and you run, then it will be further damaged and your payoffs are as follows:
a. Draw the decision tree for this problem.
b. What is your best choice of action and its expected payoff?
You can gather some more information by having more tests, and you can gather more information about whether you'll win the race by talking to your coach.
c. What is the value of perfect information about the state of your leg?
d. What is the value of perfect information about whether you'll win the tournament?
e. As stated previously, the probability that your leg is broken and the probability that you will win the tournament are independent. Can you use a decision tree in the case that the probability that you will win the race depends on whether your leg is broken?