ii) Suppose 70% of all companies are classified as small companies and the rest as large companies. Suppose further, 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 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?
The prior probabilities that the company is a large company or a small company are 0.3 and 0.7.
The revised probabilities that the company is large or small are:
"P(L|T) = 0.3\u00d70.82\/(0.3\u00d70.82 + 0.7\u00d70.18) = 0.6613."
"P(S|T) = 0.7\u00d70.18\/(0.3\u00d70.82 + 0.7\u00d70.18) = 0.3387."
The overall percentage of companies that offer training is:
"P(T) = 0.3\u00d70.82 + 0.7\u00d70.18 = 0.372."
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