In a certain Algebra and Trigonometry class, there are 22 male freshmen, 1 female freshmen, 12 male sophomores, and 3 female sophomores. If a person is selected randomly fr the group, find the probability that the selected person is a freshman or female.
To find the probability that a randomly selected person from the group is either a freshman or female, we can first count the total number of people in each category, then add those numbers together to get the probability of the combined event. Since a female freshman is both a freshman and female, we need to ensure we don't double-count her.
The total number of freshmen (male and female) is 22 male freshmen + 1 female freshman = 23 freshmen.
The total number of females (freshmen and sophomores) is 1 female freshman + 3 female sophomores = 4 females.
However, since 1 female freshman is included in both categories, we don't want to count her twice. By adding the freshmen and females together, we've counted the one female freshman twice. So we subtract her from the total to ensure that each person is only counted once.
Therefore, the combined number of unique freshmen or female students is 23 freshmen + 4 females - 1 female freshman = 26.
Now let's find the total number of students in the class to determine the probability.
Total students = 22 male freshmen + 1 female freshman + 12 male sophomores + 3 female sophomores
Total students = 22 + 1 + 12 + 3
Total students = 38
The probability that a randomly selected person is a freshman or female is the number of freshmen or females divided by the total number of students.
Probability = Number of freshmen or females / Total number of students
Probability = 26 / 38
To simplify the fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD). However, in this case, there isn't a number greater than 1 that divides both 26 and 38 evenly, so the fraction is already in its simplest form.
Therefore, the probability is 26/38, which can also be expressed as a decimal by dividing 26 by 38.
Probability ≈ 0.6842
So, the probability that a randomly selected person from the class is either a freshman or female is approximately 0.6842 or 68.42%.