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. Write as a fraction
To calculate the probability that the selected person is a freshman or female, we should first determine how many freshmen and how many females there are, and then use those numbers to calculate the probability.
Number of freshmen (both male and female) = Number of male freshmen + Number of female freshmen
Number of freshmen = 22 (male) + 1 (female) = 23
Number of females (both freshmen and sophomores) = Number of female freshmen + Number of female sophomores
Number of females = 1 (freshman) + 3 (sophomore) = 4
Next, we count the total number of students in the class.
Total number of students = Number of male freshmen + Number of female freshmen + Number of male sophomores + Number of female sophomores
Total number of students = 22 + 1 + 12 + 3 = 38
Now, we want the probability that the chosen person is either a freshman or a female. We should be careful to count the female freshmen only once, because they are both freshmen and female.
Total number of freshmen OR females (without counting female freshmen twice) =
Number of freshmen + Number of non-freshman females (since we've already counted the female freshman)
Total number of freshmen OR females = 23 (freshmen) + (4 (females) - 1 (female freshman already counted)) =
23 + (4 - 1) = 23 + 3 = 26
Therefore, the probability that a randomly selected person is either 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, we can divide both the numerator and the denominator by their greatest common divisor (GCD). However, since 26 and 38 do not share any common factors besides 1, the fraction cannot be simplified further.
So the probability as a fraction in its simplest form is:
Probability = 26 / 38
The fraction can be expressed in decimal form as approximately 0.684, but since you requested it as a fraction, we will leave it as 26/38.