The Organizational Development Journal (Summer 2006) reported on the results of a survey of human resource officers (HROs) at major firms. The focus of the study 3 was employee behaviour, namely absenteeism, promptness to work, and turnover. The study found that 55% of the HROs had problems with absenteeism. Also, 41% of the HROs had problems with turnover. Suppose that 22% of the HROs had problems with both absenteeism and turnover. (a) Find the probability that a HRO selected from the group surveyed had problems with employee absenteeism or employee turnover. (b) Find the probability that a HRO selected from the group surveyed did not have prob- lems with employee absenteeism. (c) Find the probability that a HRO selected from the group surveyed did not have prob- lems with employee absenteeism nor with employee turnover.

(a) = 0.74.

(b) = 0.45.

(c) = 0.26.

Step-by-step explanation:

If events X and Y are two events (subset of a sample space S) and are not disjoint, then

This is known as the addition rule or addition theorem.

The formula to compute the probability of neither X nor Y is:

The probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.

Complement of an event is, 1 – P.

Denote the events as follows:

A = a HRO has problems with absenteeism

T = a HRO has problems with turnover

The information provided is:

(a)

Compute the value of P (A ∪ T) as follows:

Thus, the probability that a HRO selected from the group surveyed had problems with employee absenteeism or employee turnover is 0.74.

(b)

Compute the value of as follows:

Thus, the probability that a HRO selected from the group surveyed did not have problems with employee absenteeism is 0.45.

(c)

Compute the value of as follows:

Thus, the probability that a HRO selected from the group surveyed did not have problems with employee absenteeism nor with employee turnover is 0.26.