Answer:
a) p(small) = 0.126
p(large) = 0.246
b) p(small) = 0.6613
p(large) = 0.3387
c) 37.2%
Explanation:
<u>A) determine that the company picked is a large company or small company</u>
<u>condition : the company provides training to its employees</u>
Given data:
p( small ) = 0.7, p( large ) = 0.3, p( training ∩ small ) = 0.18, p( training ∩ large ) = 0.82 , p( No-training ∩ small ) = 0.82 , p( no-training ∩ large ) = 0.18
<em>A) </em><em>hence the probability of picking a small company that provides training </em>
P( small | training ) = P(Training ∩ Small)* P(Small) = 0.18 * 0.7 = 0.126
<em>Probability of picking a large company that provides training </em>
P( large | training ) = P(training ∩ Large) *P(Large) = 0.82 * 0.3 = 0.246
<u>B) Determine the revised probabilities that company picked is large or small </u>
Revised probability for a large company; P( large | training )
P(Large | training) = P(Large ∩ training) / P(training)
= 0.246 / ( 0.126 + 0.246 ) = 0.6613
P( small | training ) = P( small ∩ training ) / P(training )
= 0.126 / ( 0.126 + 0.246 ) = 0.3387
<u>C) Overall percentage of companies that offer training </u>
p( training ) = 0.126 + 0.246 = 0.372 = 37.2%
