The probability of event B given event A has occurred is given by:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
In this case let A be the event "the student got an A" and let B be the event "the student is a male".
From the two-way table we notice that 24 out of 54 students got an A, then we have:
[tex]P(A)=\frac{24}{54}=\frac{4}{9}[/tex]
Also, from the two-way table we notice that 10 students area male and got an A, then we have:
[tex]P(A\cap B)=\frac{10}{54}=\frac{5}{27}[/tex]
Now, we plug the values in the expression for the conditional probability:
[tex]P(B|A)=\frac{\frac{5}{27}}{\frac{4}{9}}=\frac{(5)(9)}{(4)(27)}=\frac{45}{108}=\frac{5}{12}[/tex]
Therefore, the probability that the student was male given they got an A is 5/12
