PROBLEM 4. You are trying to determine whether to invest in Microsoft. From all of your research, you have determined that Microsoft's next product will succeed with a probability of 0.6. If the product succeeds, then the stock price (ticker: MSFT) will go up with a probability of 0.9, and otherwise the stock price will go down. If the product doesn't succeed, then the stock price will go up with a probability of 0.3 and otherwise will go down. After the stock price changes, the CEO will either stay or be replaced by a new CEO. If the stock price went up, then the probability of a new CEO is 0.1, whereas if the stock price went down the probability of a new CEO is 0.4. (a) Draw a decision tree diagram for all possible outcomes. You do not need to list the probability for final outcomes, just list probabilities on edges between nodes. (b) What is the probability that there will be a new CEO? (c) You have just received insider information about the product, and now you are sure that the product will succeed. What is the new probability that there will be a new CEO