Question

CONDITIONAL PROBABILITY ASSISTANCE

Answer 1

Consider such events:

A - selected student is freshmen

B - selected student is girl

$A\cap B$ - selected student is freshman is girl

$A|B$ - choosen girl is freshmen.

Use formula $Pr(A|B)=\dfrac{Pr(A\cap B)}{Pr(B)}$.

From the table you can see that girls that are freshmen are 4 from all 30 people, then $Pr(A\cap B)=\dfrac{4}{30}$. There are 18 girls, then $Pr(B)=\dfrac{18}{30}$. Substitute into the formula:

$Pr(A|B)=\dfrac{\frac{4}{30} }{\frac{18}{30} }=\dfrac{4}{18} =\dfrac{2}{9}$.

Answer: $Pr(A|B)=\dfrac{2}{9}$.