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In a certain Algebra 2 class of 30 students, 16 of them play basketball and 10 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
Answer:

In a certain Algebra $2$ class of $30$ students, $16$ of them play basketball and $10$ of them play baseball. There are $8$ students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball? $\newline$ Answer:

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Probability of independent and dependent events

Full solution

Q. In a certain Algebra

2

class of

30

students,

16

of them play basketball and

10

of them play baseball. There are

8

students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

\newline

Answer:

Determine Total Students: First, let's determine the total number of students who play either basketball or baseball. Since some students might play both sports, we cannot simply add the number of basketball players to the number of baseball players. We need to use the principle of inclusion-exclusion.
Principle of Inclusion-Exclusion: According to the principle of inclusion-exclusion, the number of students who play basketball or baseball is equal to the number of basketball players plus the number of baseball players minus the number of students who play both sports.
Find Students Who Play Both: We can find the number of students who play both sports by subtracting the number of students who play neither sport from the total number of students, and then subtracting the number of students who play only one sport (basketball or baseball).
Calculate Students Who Play One Sport: The number of students who play only one sport is the total number of students minus the number of students who play neither sport: $30$ students $-$ $8$ students $=$ $22$ students.
Calculate Students Who Play Both: Now, we subtract the number of students who play only one sport from the sum of basketball and baseball players to find the number of students who play both: $16$ basketball players $+$ $10$ baseball players\) $-$ $22$ students $=$ $4$ students who play both sports.
Apply Inclusion-Exclusion Principle: Using the principle of inclusion-exclusion, the number of students who play basketball or baseball is: $16$ basketball players + $10$ baseball players - $4$ students who play both = $22$ students.
Calculate Probability: The probability that a student chosen randomly from the class plays basketball or baseball is the number of students who play basketball or baseball divided by the total number of students in the class.
Final Probability Calculation: Calculating the probability: $22$ students who play basketball or baseball $/$ $30$ total students $=$ $11/15$ .

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