Question

In a certain Algebra 2 class of 30 students, 14 of them play basketball and 7 of them play baseball. There

are 11 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball

Answer 1

Using the principle of inclusion-exclusion, we find 10 students in the class play both basketball and baseball. The probability that a student chosen at random plays both sports is 10 out of 30, which simplifies to 1/3 or about 0.3333.

Step-by-step explanation:

The question pertains to the calculation of probability concerning students engaged in multiple sports activities.

The class comprises 30 students, with 14 playing basketball, 7 playing baseball, and 11 students who do not play either sport.

We need to determine the probability that a randomly selected student plays both basketball and baseball.

First, we use the principle of inclusion-exclusion to find the number of students who play both sports, which is given by both = basketball + baseball - neither.

Substituting the given numbers we have: both = 14 + 7 - 11 = 10 students. Therefore, 10 students play both sports.

To calculate the probability that a randomly chosen student plays both sports, we divide the number of students who play both sports by the total number of students in the class.

The probability is 10/30, which simplifies to 1/3 or approximately 0.3333.