please explain if possible Suppose 70% of all companies are classified as small

Question

please explain if possible Suppose 70% of all companies are classified as small companies and the rest as large companies. Suppose further that 82% of large companies provide training to employees, but only 18% of small companies provide training. A company is randomly selected without knowing if it is a large or small company; however, it is determined that the company provides training to its employees. What are the prior probabilities that the company is a large company or a small company? What are the revised probabilities that the company is large or small? Based on your analysis, what is the overall percentage of companies that offer training?

Explanation / Answer

a) prior probabilities that the company is a large company or a small company

P( large ) = 0.30

P( Small) = 0.30

b) revised probabilities that the company is large or small

P( Large/Training) = (0.82*0.30)/(0.82*0.30+0.18*0.70) = 0.66129

P( Small/Training) = (0.18*0.70)/(0.82*0.30+0.18*0.70) = 0.33871

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