Suppose you are modeling GNP, and you believe that the probability that GNP will expand if interest rates fall is 70%; if interest rates stay constant, you believe that there is a 29% chance of expanding GNP; if interest rates increase, you believe that there is a 1% chance of GNP expanding. You think that the likelihood of interest rates falling is 60%; of staying the same is 30%; of increasing is 10%. What is the unconditional probability of GNP expanding?
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A. B. C. D.C
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 0.70 * 0.60 + 0.29 * 0.30 + 0.01 * 0.10 = 0.42 + 0.087 + 0.001 = 0.508.