in a certain algebra 2 class of 27 students, 17 of them play basketball and 19 of them play baseball. there…

in a certain algebra 2 class of 27 students, 17 of them play basketball and 19 of them play baseball. there are 2 students who play neither sport. what is the probability that a student chosen randomly from the class plays both basketball and baseball?

in a certain algebra 2 class of 27 students, 17 of them play basketball and 19 of them play baseball. there are 2 students who play neither sport. what is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer

Explanation:

Step1: Find the number of students who play at least one sport

Total students (n(T)=27). Students who play neither (n(N) = 2). So, students who play at least one sport (n(A\cup B)=n(T)-n(N)=27 - 2=25)

Step2: Use the formula (n(A\cup B)=n(A)+n(B)-n(A\cap B))

Let (n(A)) (basketball players) ( = 17), (n(B)) (baseball players) (=19) and (n(A\cup B) = 25) Substitute into the formula: (25=17 + 19-n(A\cap B))

Step3: Solve for (n(A\cap B))

Rearrange the equation: (n(A\cap B)=17 + 19-25) (n(A\cap B)=11)

Step4: Calculate the probability

Probability (P=\frac{n(A\cap B)}{n(T)}) Since (n(A\cap B) = 11) and (n(T)=27), (P=\frac{11}{27})

Answer:

(\frac{11}{27})