An expert economist forecasts that the probability of having a recession next year is 20%, a slow growth is 45%, and a fast growth is 35%. From experience when the economy is in a recession, your business has a 5% chance of losing $1,000,000, a 25% chance of losing $300,000, a 50% chance of breaking even, and a 20% chance of making $10,000. When the economy grows slowly, your business has a 25% chance of losing $100,000, a 40% chance of breaking even, and a 35% chance of making $150,000. When the economy grows rapidly, your business has a 45% chance of making $500,000, a 40% chance of making $200,000, and a 15% chance of breaking even.
a) What is the probability that your business will make a profit next year?
b) What is the expected profit next year? What is the risk?
c) If your business makes a profit next year, what is the probability that the economy is in a recession?
d) Are the events recession and breaking even mutually exclusive? Are the events slow growth and making a profit independent? Explain!