In a certain Algebra 2 class of 28 students, 17 of them play basketball and 9 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
To find the probability that a student plays both basketball and baseball, we need to know the number of students who play both sports and the total number of students in the class.
From the given information, we know that there are 28 students in the class, 17 of them play basketball, 9 of them play baseball, and 5 students play neither of the sports.
To find the number of students who play both sports, we need to find the intersection of the basketball and baseball players.
We can use the principle of inclusion-exclusion to find the number of students who play both sports:
Number of students who play both sports = Total number of students who play basketball + Total number of students who play baseball - Total number of students who play neither sport.
Number of students who play both sports = 17 + 9 - 5 = 21.
Therefore, there are 21 students who play both basketball and baseball.
The probability of randomly choosing a student who plays both sports can be found by dividing the number of students who play both sports by the total number of students in the class:
Probability = Number of students who play both sports / Total number of students
Probability = 21 / 28 = 3 / 4.
Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is 3/4 or 0.75.