An analyst expects that 20% 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) 69%. C) 26%. D) 44%.
first branch is 20 up and 80 down… branch from 20 is 90 up and 10 down branch from 80 is 10 up and 90 down. .2* .9= .18 .8*.1= .08 .18/.26= 69! sixty nine! haaaaaa always guess for the 69 option. cfa testers love that number
.2* .9= .18 .8*.1= .08 Ok I got that far, .18/.26. What is that from?
http://i30.tinypic.com/15nothw.jpg edit: oops i solved a different question, but it is almost identical apply the same principles An analyst has developed a ratio to identify companies expected to experience declining earnings per share (EPS). Research shows that 70 percent of firms with declining EPS have a negative ratio, while only 20 percent of firms not experiencing a decline in EPS have a negative ratio. The analyst expects that 10 percent of all publicly traded companies will experience a decline in EPS next year. The analyst randomly selects a company and its ratio is negative. Based on Bayes’ theorem, the posterior probability that the company will experience an EPS decline next year is closest to: A. 14%. B. 28%. C. 30%. D. 50%.
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so the total odds of you getting a negative ratio is .18 plus .08… = .26… so if thats the total odds…what are the odds of it coming from the .18 branch or .08 branch? well its .18/.26 for the 20% branch and .08 for the 80% branch… get the scwheser. bayes section, they break it down pretty good