Problem 5 [15 points - 6 + 3 + 3 + 3] Financial analysts conduct risk assessments based on two events. Event M states that the mortgage demand will grow and event R is that the interest rate will go down. Their risk assessments resulted in probabilities shown below. . P [R] = 0.20 . P [M] = 0.40 . Probability that at least one of these two events will occur is P[MUR - 0.46 1. Fill all joint and marginal probabilities in the table below and then answer questions below using probability rules. 2. Are events,(M, R) independent? 3. Find probability that mortgage demand will grow, given that the interest rate decreases, P [M| R] 4. How likely the interest rate will decrease, given that the mortgage demand grows, P [RIM] M M' Marginal R PIMOR = PIM'nR]- P [R] = 0.20 R' P[MOR'] = PIM'nR]= P [R] = Marginal P [M] - 0.40 PIM]- Solution