Explanation:
The probability of general practitioners will be given below as
[tex]Pr(G)=\frac{4}{17}[/tex]
The probability of people under the age of 45 is given below as
[tex]Pr(U)=\frac{7}{17}[/tex]
The probability of people that are both general practitioners and under the age of 45 is given below as
[tex]Pr(G\cap U)=\frac{2}{17}[/tex]
Hence,
To calculate the probability that you are randomly assigned a general practitioner or doctor under the age of 45, we will use the formula below
[tex]Pr(G\cup C)=Pr(G)+Pr(U)-Pr(G\cap C)[/tex]
By substituting the values, we will have
[tex]\begin{gathered} Pr(G\cup C)= Pr(G)+Pr(U)-Pr(G\operatorname{\cap}C) \\ Pr(G\cup C)=\frac{4}{17}+\frac{7}{17}-\frac{2}{17} \\ Pr(G\cup C)=\frac{9}{17} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow\frac{9}{17}[/tex]
