WE need to find the probability ([tex] \frac{Junior}{girl} [/tex])
We know Probability ( [tex] \frac{A}{B} [/tex]) = [tex] \frac{P(A and B)}{P(B)} [/tex]
P ( [tex] \frac{Junior}{Girl} [/tex]) = [tex] \frac{P(Junior and girl)}{P(girl)} [/tex]
First we find P(Girl)
From the table we can see that we have 18 girls out of (12+18=30) students
So P(Girl) = [tex] \frac{18}{30} [/tex]
Now we find the intersection of Junior and Girl
WE look at the Junior row and girls column that is 3
{P(Junior ∩ Girl) = [tex] \frac{3}{30} [/tex]
P ( [tex] \frac{Junior}{Girl} [/tex]) = [tex] \frac{P(Junior and girl)}{P(girl)} [/tex]
P ( [tex] \frac{Junior}{Girl} [/tex]) = [tex] \frac{\frac{3}{30}}{\frac{18}{30}} [/tex]
= [tex] \frac{3}{18} = \frac{1}{6} [/tex]
