The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We want to calculate the probability the student is a male given that it's a sophomore. Since we already know the student is a sophomore, the possible outcomes are only male sophomores(6) and female sophomores(4) and the favourable outcomes are the male sophomores(6), therefore, this probability is:
[tex]P(Male|Sophomore)=\frac{6}{6+4}=\frac{6}{10}=\frac{60}{100}=60\%[/tex]The probability the student is a male given that it's a sophomore is 60%.