in a certain algebra 2 class of 30 students, 11 of them play basketball and 23 of them play baseball. there…

in a certain algebra 2 class of 30 students, 11 of them play basketball and 23 of them play baseball. there are 3 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 30 students, 11 of them play basketball and 23 of them play baseball. there are 3 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 number of students who play at least one sport

Total students - students who play neither sport = 30 - 3 = 27.

Step2: Use the inclusion - exclusion principle

Let (A) be the set of basketball players and (B) be the set of baseball players. We know (n(A)=11), (n(B)=23) and (n(A\cup B) = 27). By the formula (n(A\cup B)=n(A)+n(B)-n(A\cap B)), we can find (n(A\cap B)). So (n(A\cap B)=n(A)+n(B)-n(A\cup B)=11 + 23-27=7).

Step3: Calculate the probability

Probability (P=\frac{\text{Number of students who play both}}{\text{Total number of students}}=\frac{7}{30}).

Answer:

(\frac{7}{30})