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

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} Division & Agree & Disagree & Total \\ \hline Production & 17 & 23 & 40 \\ \hdashline Office & 8 & 2 & 10 \\ \hdashline Total & 25 & 25 & 50 \end{array}$$

4.2.1)

$$P(A)={40 \over 50}={4 \over 5}=0.8$$

$$P(A^C)=1-0.8=0.2$$

4.2.2)

$$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)=$$

$$={40 \over 50}+{25 \over 50}-{17 \over 50}={24 \over 25}=0.96$$

4.2.3)

$$P(C\ and \ D)={2 \over 50}={1 \over 25}=0.04$$

4.2.4)

$$P(C|D)={2 \over 25}=0.08$$