In a certain Algebra and Trigonometry class, there are 6 male freshmen, 18 female freshmen, 4 male sophomores, and 1 female sophomores. If a person is selected randomly from the group, find the probability that the selected person is a freshman or female.
To find the probability that the selected person is a freshman or female, we first need to find the total number of individuals that fall into either of those categories, and then divide by the total number of individuals in the class.
The number of freshmen is the sum of male and female freshmen:
Number of freshmen (male + female) = 6 male freshmen + 18 female freshmen = 24 freshmen
The number of females (including both freshmen and sophomores) is:
Number of females (freshmen + sophomores) = 18 female freshmen + 1 female sophomore = 19 females
Note that when we add the number of freshmen and females together, we do not want to double-count the female freshmen, as they are part of both groups. To avoid this, we will first find the total number of individuals in the class and then subtract the number of male sophomores (since male sophomores are neither freshmen nor female, so they are the complement in this group).
The total number of individuals in the class is:
Total number of students = 6 male freshmen + 18 female freshmen + 4 male sophomores + 1 female sophomore = 29 students
Since the 18 female freshmen have already been counted in both the freshmen and female categories, we don't add these numbers together when calculating the probability. Instead, we look at the number of males that aren't freshmen (which is 4 male sophomores) and subtract it from the total number of students to avoid double-counting:
Number of students who are either freshmen or female = Total number of students - Number of male sophomores
Number of students who are either freshmen or female = 29 - 4 = 25 students
Now, calculate the probability of selecting a freshman or female:
Probability of selecting a freshman or female = Number of students who are either freshmen or female / Total number of students
Probability of selecting a freshman or female = 25 / 29
So, the probability that the selected person is a freshman or female is 25/29.