It is given that,
[tex]\begin{gathered} Number\text{ of vaccination = 6} \\ Number\text{ of wellness checks = 3} \\ Number\text{ of ill children = 5} \end{gathered}[/tex]The required probability is given as,
[tex]P(Vaccinations)\text{ = }\frac{Number\text{ of vaccinations }}{Total\text{ number of files}}[/tex]Therefore,
[tex]\begin{gathered} P(Vaccinations)\text{ = }\frac{6}{14} \\ P(Vaccinations)\text{ = 0.4285} \end{gathered}[/tex]