In a certain Algebra 2 class of 20 student, 14 of them play basketball and 5 of them play baseball. There are 4 students who play neither sports. What is the probably that a student chosen randomly from the class plays basketball and baseball?
To find the probability that a student chosen randomly from the class plays both basketball and baseball, we first need to find the total number of students who play either basketball or baseball.
The total number of students who play basketball is 14, and the total number of students who play baseball is 5. However, we have counted the students who play both sports twice (once in each group), so we need to subtract that number to avoid double counting.
Let B be the number of students who play basketball, and let b be the number of students who play baseball. Then, the total number of students who play either basketball or baseball can be calculated as:
B + b - (students who play both basketball and baseball) + (students who play neither sport) = 20
14 + 5 - x + 4 = 20
19 - x + 4 = 20
23 - x = 20
-x = -3
x = 3
So, there are 3 students who play both basketball and baseball.
The probability that a student chosen randomly from the class plays both basketball and baseball is:
3/20 or 0.15 or 15%