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Explanation:
Using the new information, we can use Bayes' formula to update the probability.
P(economy does not expand | tech does not outperform) = P(economy does not expand and tech does not outperform) / P(tech does not outperform)
P(economy does not expand) = 1.00 − P(economy does expand) = 1.00 − 0.60 = 0.40
P(tech does not outperform | economy does not expand) = 1.00 − P(tech does outperform | economy does not expand) = 1.00 − 0.10 = 0.90
P(economy does not expand and tech does not outperform) = P(tech does not outperform | economy does not expand) × P(economy does not expand) = 0.90 × 0.40 = 0.36
P(economy does expand and tech does not outperform) = P(tech does not outperform | economy does expand) × P(economy does expand) = 0.30 × 0.60 = 0.18
P(tech does not outperform) = P(tech does not outperform and economy does not expand) + P(tech does not outperform and economy does expand) = 0.36 + 0.18 = 0.54
P(economy does not expand | tech does not outperform) = P(economy does not expand and tech does not outperform) / P(tech does not outperform) = 0.36 / 0.54 = 0.67
(Book 2, Module 12.2, LO 12.g)
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Question 86
An economist estimates a 60% probability that the economy will expand next year. The technology sector has a 70% probability of outperforming the market if the economy expands and a 10% probability of outperforming the market if the economy does not expand. Given the new information that the technology sector will not outperform the market, the probability that the economy will not expand is closest to:
A
67%.
B
54%.
C
33%.
D
48%.