In a certain Algebra and Trigonometry class, there are 4 male freshmen, 21 female freshmen, 12 male sophomores, and 12 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 need first to determine the total number of freshmen and the total number of females in the class, and then add these numbers together. However, we have to subtract the overlap (female freshmen) to avoid double-counting, since the overlap represents individuals who are counted in both categories.
First calculate the total number of freshmen:
Number of male freshmen = 4
Number of female freshmen = 21
Total number of freshmen = 4 (male freshmen) + 21 (female freshmen) = 25
Next, calculate the total number of females (both freshmen and sophomores):
Number of female freshmen = 21
Number of female sophomores = 12
Total number of females = 21 (female freshmen) + 12 (female sophomores) = 33
Since female freshmen are counted in both categories (freshmen and females), we subtract the number of female freshmen once to get the correct count:
Total number of freshmen or females = Total number of freshmen + Total number of females - Number of female freshmen
Total number of freshmen or females = 25 + 33 - 21 = 37
Finally, calculate the total number of students in the class:
Number of male freshmen = 4
Number of female freshmen = 21
Number of male sophomores = 12
Number of female sophomores = 12
Total number of students = 4 (male freshmen) + 21 (female freshmen) + 12 (male sophomores) + 12 (female sophomores)
Total number of students = 49
Now, we can find the probability that the selected person is a freshman or female:
Probability = (Total number of freshmen or females) / (Total number of students)
Probability = 37 / 49
This is the probability that a person selected randomly from the group is a freshman or female.