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In a certain Algebra $2$ class of $24$ students, $16$ of them play basketball and $7$ 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 basketball or baseball?

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Find probabilities using the addition rule

Full solution

Q. In a certain Algebra

2

class of

24

students,

16

of them play basketball and

7

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 basketball or baseball?

Calculate total students playing sports: Calculate the total number of students who play at least one sport. Since $5$ students play neither sport, subtract this from the total class size to find those who play sports.
Use inclusion-exclusion principle: Use the principle of inclusion-exclusion to find the number of students who play basketball or baseball. Add the number of basketball players to the number of baseball players, then subtract the number of students who play both sports.
Calculate probability for basketball or baseball: Calculate the probability that a randomly chosen student plays basketball or baseball. Divide the number of students who play sports by the total number of students.

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