Final answer:
To find the probability that a randomly chosen student from the class plays basketball or baseball, we calculate the union of the two sets. Since there are overlaps (students who play both), we subtract the number of students playing both from the sum of students playing each sport. The result is a probability of 17/24.
Step-by-step explanation:
The student's question pertains to the concept of probability in a typical Algebra 2 class setting. To solve for the probability that a student plays either basketball or baseball, one can use the formula for the union of two sets: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). In this scenario, P(A) is the probability of playing basketball, P(B) is the probability of playing baseball, and P(A ∩ B) is the probability of playing both.
Given that there are 15 basketball players and 7 baseball players in a class of 24 students, and 5 play both sports, we can calculate it as follows:
- P(A) = number of basketball players / total students = 15/24
- P(B) = number of baseball players / total students = 7/24
- P(A ∩ B) = number of students who play both sports / total students = 5/24
Putting these into the formula gives us:
P(A ∪ B) = (15/24) + (7/24) - (5/24)
P(A ∪ B) = (15 + 7 - 5) / 24
P(A ∪ B) = 17/24
Therefore, the probability that a student chosen at random from the class plays basketball or baseball is 17/24.