Answer to Question #110009 in Statistics and Probability for Mike

Question

A manufacturing plant conducted a survey to determine it's employees reaction toward a proposed change in working hours.a breakdown of the response is as follows: production:17 agree 23 disagree. Office:8 agree 2 disagree. Suppose an employee is chosen at random with events being defined as A:the employee works in the production team. B:the employee agreed with the proposed change. C: the employee works in the office. D: the employee disagree with the proposed change. 4.2.1) P(A). 4.2.2) P(A or B). 4.2.3)P(C and D). 4.2.4)P(c/D)

Answer 1

 A:the employee works in the production team

B:the employee agreed with the proposed change

C: the employee works in the office

 D: the employee disagree with the proposed change

4.2.1) $P(A)=\frac{Employees\ in\ production}{Total\ employees}\\$

$\bold{P(A)=\frac{40}{50}=0.8}\\$

4.2.2) $P(B)=\frac{Agreed\ employees\ }{Total\ employees}=\frac{25}{50}=0.5\\$

$P(A \cap B)=\frac{Agreed \ production\ employees\ }{Total\ employees} =\frac{17}{50}=0.34\\ P(A \cup B)=P(A)+P(B)-P(A \cap B)\\ \bold{P(A \cup B)=0.8+0.5-0.34=0.96}$

4.2.3) $P(C \cap D)=\frac{Disagreed\ office\ employees\ }{Total\ employees}\\$

$\bold{ P(C \cap D)=\frac{2}{50}=0.04}$

4.2.4) $P(D)=\frac{Disagreed\ employees}{Total\ employees}=\frac{25}{50}=0.5\\$

$P(C/D)=\frac{P(C \cap D)}{P(D)}\\ P(C/D)=\frac{0.04}{0.5}\\ \bold{P(C/D)=0.08}\\$