Suppose you are modeling long-term interest rates, and you believe that supply of corporate debt is a major contributing factor. Suppose you believe that the probability that rates will rise if supply of corporate debt rises is 60%; if the supply of corporate debt stays constant, you believe that there is a 35% chance of increasing interest rates; if the supply of corporate debt falls, you believe that there is a 5% chance of rates increasing. You think that the likelihood of corporate debt increasing is 50%; of staying the same is 40%; of dropping is 10%. What is the unconditional probability of interest rates rising?
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A. B. C. D.Explanation
We use the total probability rule: P(A), the unconditional probability, = P(A|S_1)*P(S_1) + P(A|S_2) *P(S_3) + P(A|S_3) *P(S_3), where the S_i represent mutually exclusive and exhaustive events. So the likelihood of interest rates increasing is 0.60 * 0.50 + 0.35 * 0.40 + 0.05 * 0.10 = 0.30 + 0.14 + 0.005 = 0.445.