Answer to Question #202346 in Statistics and Probability for Aasia Tariq

Question

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?

Answer 1

The prior probabilities:

70% - small companies

30% - large companies

Revised probabilities:

for small companies:

$0.7\cdot0.18=0.126$

for large companies:

$0.3\cdot0.82=0.246$

The overall percentage of companies that offer training:

$0.126+0.246=0.372$