We are asked to find the conditional probability that the student is a male given that it's a senior.
Recall that the conditional probability is given by
[tex]P\mleft(A\vert B\mright)=\frac{P\mleft(A\: and\: B\mright)}{P\mleft(B\mright)}[/tex]P(A | B) means that the probability of event A given that event B has already occurred.
Applying it to the given situation,
[tex]P(Male\vert Senior)=\frac{P(Male\: and\: Senior)}{P(Senior)}[/tex]The probability P(Male and Senior) is given by
[tex]P(Male\: and\: Senior)=\frac{n(Male\: and\: Senior)}{n(total)}=\frac{2}{30}=\frac{1}{15}[/tex]Where n(Male and Senior) is the intersection of the row "Male" and the column "Senior" that is 2
n(total) is the grand total of all the students.
Grand total = 4+3+6+4+2+6+2+3 = 30
The probability P(Senior) is given by
[tex]P(Senior)=\frac{n(Senior)}{n(total)}=\frac{5}{30}=\frac{1}{6}[/tex]Where n(Senior) is the column total of the column "Senior" that is (2 + 3 = 5)
n(total) is the grand total of all the students.
Finally, the probability that the student is a male given that it's a senior is
[tex]\begin{gathered} P(Male\vert Senior)=\frac{P(Male\: and\: Senior)}{P(Senior)} \\ P(Male\vert Senior)=\frac{\frac{1}{15}}{\frac{1}{6}}=\frac{1}{15}\times\frac{6}{1}=\frac{6}{15}=0.40=40\% \end{gathered}[/tex]Therefore, the probability that the student is a male given that it's a senior is 40%