A survey of workers in the two plants of a manufacturing fir

A survey of workers in the two plants of a manufacturing firm includes the question “How effective is management in responding to legitimate grievances of workers?” In plant 1, 48 of 192 workers respond “poor”; in plant 2, 80 of 248 workers respond “poor”. An employee of the manufacturing firm is to be selected randomly. Let A be the event “worker comes from plant 1” and let B be the event “response is ‘poor’.”

a) Find P(A), P(B), and P(A|B).

b) Are the events A and B independent?

Solution

a)

P(A) = 192/(192+248) = 0.436363636 [ANSWER]

P(B) = (48+80)/(192+248) = 0.290909091 [ANSWER]

P(A|B) = 48/(48+80) = 0.375 [ANSWER]

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b)

As we see,

P(A) =/= P(A|B)

therefore, they are not independent.