An analyst expects that 10% of all publicly traded companies will experience a d
ID: 3249070 • Letter: A
Question
An analyst expects that 10% 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 70% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 20% chance that the ratio will be negative. The analyst randomly selects a company and its ratio is negative. Based on Bayes's theorem, the posterior probability that the company will experience a decline is ______. 18% 28% 7% 3%Explanation / Answer
Let N = negative , D = Decline , N' = non negative , D' = non decline
P(D) = 0.1 ,P(D') = 1-0.1 = 0.9
p( ratio negative if decline )= p(N/D) = 0.7
p( ratio non negative if decline )=p(N' /D) = 1- 0.7 = 0.3
p(ratio negative if not decline)= p(N /D') = 0.2
p(ratio not negative if not decline) = p(N'/D')= 1 - 0.2 = 0.8
p(D/N) = ?
P(D/N) = P(D) P(N/D) / {P(D) P(N/D) + P(D') P(N/D') }
= 0.1 * 0.7 / { 0.1*0.7 + 0.9 *0.2}
= 0.07/0.25
= 0.28
= 28%
2nd option that is 28% is correct answer.