Answer to Question #110463 in Statistics and Probability for Miranda

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

4.2.1) $P(A)=\frac{Production\ employees}{Totalemployees}=\frac{40}{50}=0.8$

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

4.2.2) $P(A\cup B )=P(A)+P(B)-P(A\cap B)$

$P(A\cup B )=P(A)+P(B)-P(A|B)P(B)$

where,

$P(B)=\frac{Agreed\ employees}{Total\ employees}=\frac{25}{50}=0.5\\ P(A|B)=\frac{Agreed\ production\ employees}{Agreed\ Employees}=\frac{17}{25}=0.68\\$

$P(A\cup B )=0.8+0.5-0.68*0.5\\ P(A\cup B )=0.96\\ \bold{P(A\ or\ B )=0.96}$

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

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

4.2.3) $P(C|D)=\frac{P(C\cap D)}{P(D)}$

where,

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

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