SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} p(A\cap B)=\frac{3}{100} \\ p(B|A)=\frac{3}{20} \\ p(A)=? \end{gathered}[/tex]STEP 2: Write the formula for conditional probability
[tex]p(B|A)=\frac{p(A\cap B)}{p(A)}[/tex]STEP 3: Get the value of the requried probability
By Substitution,
[tex]\begin{gathered} \frac{3}{20}=\frac{\frac{3}{100}}{p(A)} \\ \\ \frac{3}{20}=\frac{3}{100\times p(A)} \\ Cross\text{ Multiply} \\ 3(100p(A))=3\times20 \\ 300\times p(A)=60 \\ p(A)=\frac{60}{300}=\frac{1}{5} \end{gathered}[/tex]Hencce, p(A) = 1/5
