91Ó°ÊÓ

The probability of an event is a measure of the likelihood of an event occurring when an experiment is performed. When there are just two possible outcomes, complementary occurrences occur. There is another event${\mathbf{A}}^{\mathbf{c}}$ for every event A, which ${\mathbf{A}}^{\mathbf{c}}$signifies the complimentary event.

$\mathbf{P}\mathbf{\left(}{\mathbf{A}}^{\mathbf{c}}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{–}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{.}$

Let’s take A1 as the HRO problem with employee absenteeism and A2 as the HRO problem with employee turnover.

Therefore, we get:

$$\begin{gathered} \mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{1}\mathbf{\right)}\mathbf{=}\mathbf{55}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{55}}{\mathbf{100}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{55} \end{gathered}$$

$$\begin{gathered} \mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{41}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{41}}{\mathbf{100}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{41} \end{gathered}$$

$\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{1}\mathbf{âˆ\copyright }\mathbf{A}\mathbf{2}\mathbf{)}\mathbf{=}\mathbf{22}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{22}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{22}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{1}\mathbf{\right)}\mathbf{=}\mathbf{55}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{55}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{55}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{2}\mathbf{\right)}\mathbf{=}\mathbf{41}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{41}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{41}\end{array}$

$\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{1}\mathbf{âˆ\copyright }\mathbf{A}\mathbf{2}\mathbf{)}\mathbf{=}\mathbf{22}\mathbf{\%}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{22}}{\mathbf{100}}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{22}\end{array}$

Hence, the probability that HRO had a problem with either employee absenteeism or employee turnover is:

$\begin{array}{c}\mathbf{P}\mathbf{(}\mathbf{either}\mathbf{}\mathbf{employee}\mathbf{}\mathbf{absenteeism}\mathbf{}\mathbf{or}\mathbf{}\mathbf{}\mathbf{employee}\mathbf{}\mathbf{turn}\mathbf{}\mathbf{over}\mathbf{)}\\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{–}\mathbf{P}\mathbf{(}\mathbf{neither}\mathbf{}\mathbf{employee}\mathbf{}\mathbf{absenteeism}\mathbf{}\mathbf{or}\mathbf{}\mathbf{employee}\mathbf{}\mathbf{turn}\mathbf{}\mathbf{over}\mathbf{)}\\ \mathbf{=}\mathbf{1}\mathbf{–}\mathbf{0}\mathbf{.}\mathbf{22}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{78}\end{array}$

Therefore, the required probability is 0.78.