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SOLUTION
Write out the given data from the question
[tex]\begin{gathered} \text{Total employees=550} \\ E\text{mployes playing games =169} \\ \text{Employees for swimming=233} \end{gathered}[/tex]The probabilty of an event is given by the formula
[tex]\frac{\text{ Required outcome}}{Total\text{ outcome }}[/tex]Let
The probabilty of Employing playing games be P(E)
The probabilty of Employing for swimming be P(F)
then
[tex]\begin{gathered} P(E)=\frac{\text{Number of employ}ees\text{ playing games}}{Total\text{ number of employ}ees} \\ \\ \end{gathered}[/tex]Where
Number of employees playing games =169
Total employees =550
Substituting the values, we have
[tex]P(E)=\frac{169}{550}=0.3072[/tex]Since the probability is in percentage, multiply by 100
[tex]P(E)=0.3072\times100=30.72[/tex]Hence,
The probability of employees playing game at pastime is about 31%
Similarly,
[tex]\begin{gathered} P(F)=\frac{\text{Number of swimming employ}ees}{Total\text{ employe}es} \\ \text{Where } \\ \text{Number of swimming employ}ees=233 \\ Total\text{ employe}es=550 \end{gathered}[/tex]Substituting the values, we have
[tex]P(F)=\frac{233}{500}=0.4236[/tex]Since the probability is in percentages, We multiply by 100
Hence
[tex]P(F)=0.4236\times100=42.36[/tex]Hence
The probabilty of the employes swimming at passtime is about 42%
Therefore
the probability of an employee's choosing playing games to an employee's choosing swimming is about 31% to about 42%
Answer; about 31% to about 42%(Third option)
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