In a certain Algebra and Trigonometry class, there are 10 male freshmen, 6 fernale freshmen, 4 male sophomores, and 16 female sophomores. If a person is selected randomly from the group, find the probability that the selected person is a freshman or female
There are a total of 10 male freshmen, 6 female freshmen, 4 male sophomores, and 16 female sophomores. The total number of students is 10 + 6 + 4 + 16 = 36.
The probability of selecting a freshman or female is the sum of the probabilities of selecting a freshman and selecting a female, minus the probability of selecting a freshman who is also female (to avoid counting them twice).
The probability of selecting a freshman is (10 + 6) / 36 = 16 / 36.
The probability of selecting a female is (6 + 16) / 36 = 22 / 36.
The probability of selecting a freshman who is also female is 6 / 36.
Therefore, the probability of selecting a freshman or female is (16 / 36) + (22 / 36) - (6 / 36) = 38 / 36 = 19 / 18.
The probability that the selected person is a freshman or female is 19 / 18.