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 70% chance that this ratio will be negative. If the company is not headed for a decline, there is a 15% chance that the ratio will be negative. The analyst randomly selects a company and its ratio is negative. What is the posterior probability that the company will experience a decline?
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