WE need to find the probability ([tex] \frac{Junior}{Boy} [/tex]
We know [tex] P(\frac{A}{B})= \frac{P(A and B)}{P(B)} [/tex]
P([tex] \frac{Junior}{Boy} [/tex])=[tex] \frac{P(Junior and Boy)}{(Boy)} [/tex]
First we find P(Boy)
From the table we can see that we have 12 boys out of (12+18=30) students
So P(Boy) = [tex] \frac{12}{30} [/tex]
Now we find the intersection of Junior and Boy
WE look at the Junior row and boys column that is 2
{P(Junior ∩ Boy) = [tex] \frac{2}{30} [/tex]
P([tex] \frac{Junior}{Boy} [/tex])=[tex] \frac{P(Junior and Boy)}{(Boy)} [/tex]
P([tex] \frac{Junior}{Boy} [/tex])= [tex] \frac{\frac{2}{30}}{\frac{12}{30}} [/tex]
= [tex] \frac{2}{12} [/tex] = [tex] \frac{1}{6} [/tex]
P([tex] \frac{Junior}{Boy} [/tex]) = [tex] \frac{1}{6} [/tex]
