5. Bayes\' Rule Suppose you just started a new job with benefits, and you are tr

Question

5. Bayes' Rule Suppose you just started a new job with benefits, and you are trying to decide lh 401(k). You figure there is a 70% chance the economy will be good and should invest in otherwise you will invest in less risky bond funds. Your company's plan admini arted a new job with benefits, and you are trying to decide how to invest your you will invest in less risky bond funds. Your company's plan administrator offers help in decidin subsidizes the cost somewhat have leveled off do some research on the advisers, and find that when the future economy was good, the planner predicted it correctly 85% of the time, when the economy was bad, the planner predicted it correctly 75% of the time. You decide to spring for paying for their advice, and they said the future economy will be good. What is the chance that the future economy will be good given the planner's forecast? g, but they cost more money than you want to spend at the moment, even though the company . You decide it might be worthwhile, since the Trump bump' seems to somewhat and the future economy seems more uncertain now than 6 months ago. You You may use either a table or a tree, whichever you feel comfortable with. (20 pts. -you might want to do the exercises on conditional probability first.)

Explanation / Answer

We have given that

P(Economy is good ) =0.70, P(Economy is not good ) = 0.30

P(Correctly predicted/Economy is good ) =0.85

P(Correctly predicted/Economy is not good ) =0.75

We need to calculate

P(Economy is good/Correctly Predicted) = (0.85*0.70)/(0.85*0.70+0.75*0.30) = 0.7256

So, answer is 0.7256

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