In a certain Algebra and Trigonometry class, there are 4 male freshmen, 12 female freshmen, 10 male sophomores, and 11 female sophomores. If a person is selected randomly from the group, find the probability that the selected person is a freshman or female. (Type an integer or a simplified fraction.)
The total number of students in the class is $4+12+10+11=37$. There are 12 female freshmen, so the probability that the selected person is a female freshman is $\dfrac{12}{37}$. There are 12 female freshmen, 10 male sophomores, and 11 female sophomores, for a total of $12+10+11=33$ freshmen. The probability that the selected person is a freshman is $\dfrac{33}{37}$. Since the person being selected must be a freshman or female, we must add the two probabilities together to get $\dfrac{12}{37}+\dfrac{33}{37}=\dfrac{45}{37}$. However, $\dfrac{45}{37}=\boxed{1\dfrac{8}{37}}$ does not simplify into an integer or simplified fraction, therefore our final answer will be $2$ if we consider $2$ as a simplified fraction.
