A finance analyst expects that 30% 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 95% 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 with a negative ratio. Based on Bayes' theorem, the posterior probability that the company will experience a decline is _____
A. between 60% and 65%
B. < 50%
C. between 55% and 60%
D. > 70%
E. between 65% and 70%
F. between 50% and 55%
