When the economic situation is “high,” a certain economic indicator rises with probability 0.6. When the economic situation is “medium,” the economic indicator rises with probability 0.3. When the economic situation is “low,” the indicator rises with probability 0.1. The economy is high 15% of the time, it is medium 70% of the time, and it is low 15% of the time. Given that the indicator has just gone up, what is the probability that the economic situation is high?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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When the economic situation is “high,” a certain economic indicator rises
with probability 0.6. When the economic situation is “medium,” the economic indicator rises with probability 0.3. When the economic situation is “low,” the indicator rises with probability 0.1. The economy is high 15% of the time, it is medium 70% of the time, and it is low 15% of the time. Given that the indicator has just gone up, what is the probability that the economic situation is high?

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