# Bayes theorem Probability and test question

Hi all, I am still struggling with baye’s theorem. Is there a good chances of this being examined. How are you guys managing this inversion concept? An analyst expects that 20 percent of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes’ theorem, the updated probability that the company will experience a decline is: A) 18%. B) 26%. C) 44%. D) 69%. S

P(decline) = .2 P(Ratio Negative if decline) = 0.9 P(Ratio Non-Negative if decline) = 1 - 0.9 = 0.1 P(Ratio Negative if No decline) = 0.1 P(Ratio Non-Negative if No decline) = 1-0.1 = 0.9 So if you drew a tree P(Decline)----Negative----Non Negative 0.2-------------0.9-------------0.1 Updated P—0.18-------------0.02 P(No Decline)–Negative—Non-Negative 0.8------------- 0.1------------- 0.9 Updated P----- 0.08-------------0.72 Company had a negative ratio So total P(negative ratio): 0.18 + 0.08 = 0.26 Out of this --> 0.18 is when the company had a decline So updated probability company had a decline = 0.18 / 0.26 = 0.69 Ans D

Thanks that def helped me out.