You work for a company that is frequently involved in negotiations to acquire companies from their current owners. You have been invited to be a guest on the popular television game show Let's Make a Deal.Your boss has agreed that you can participate on the game show during business hours because you might learn something that would be valuable in future business negotiations.

• You are now on the game show. The following events have occurred to this point:
• The game show host showed you three doors, labeled Door #1, Door #2, and Door #3 and told you that behind one of the doors is the grand prize of $100,000. The other two doors contain smaller prizes of no more than $20,000. You assume that the host knows which door has the $100,000.
• You were told to choose one of the doors, and you randomly chose Door #1.
• The host subsequently opened Door #2 and showed you that it contains a smaller prize of $20,000.
• He has given you the following choice. You can keep what is behind Door #1 (your initial choice). You can trade it for the $20,000 behind Door #2, or you can trade it for the unknown contents behind Door #3.
• You want to go for the grand prize of $100,000. Thus you must decide whether to keep Door #1 or trade it for Door #3.

1. You initially selected Door #1. Prior to seeing the contents behind Door #2, what was the probability that Door #1 contained the grand prize? What was the probability that Door #1 did not contain the grand prize (i.e., the grand prize was behind one of the other two doors)?

2. The host subsequently showed you that Door #2 contained $20,000 and gave you the choice to keep what was behind Door #1 or to trade it for what was behind Door #3. What should you do or does it matter (assuming you want to go for the grand prize)?

3. Your boss let you participate in the game show because she thought you might learn something that would be of value to your company. Does your experience on the game show suggest any general principles that might be useful in managerial situations? Explain.