Consider such events:
A - selected student is freshmen
B - selected student is girl
[tex] A\cap B [/tex] - selected student is freshman is girl
[tex] A|B [/tex] - choosen girl is freshmen.
Use formula [tex] Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)} [/tex].
From the table you can see that girls that are freshmen are 4 from all 30 people, then [tex] Pr(A\cap B)=\dfrac{4}{30} [/tex]. There are 18 girls, then [tex] Pr(B)=\dfrac{18}{30} [/tex]. Substitute into the formula:
[tex] Pr(A|B)=\dfrac{\frac{4}{30} }{\frac{18}{30} }=\dfrac{4}{18} =\dfrac{2}{9} [/tex].
Answer: [tex] Pr(A|B)=\dfrac{2}{9} [/tex].
