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In a certain Algebra 2 class of 29 students, 9 of them play basketball and 15 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 basketball or baseball?
Answer:

In a certain Algebra $2$ class of $29$ students, $9$ of them play basketball and $15$ 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 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

29

students,

9

of them play basketball and

15

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 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.
Calculate Students Playing Sports: We know that there are $11$ students who play neither sport. Therefore, the number of students who play either basketball or baseball, or both, is the total number of students minus those who play neither sport. $\newline$ Number of students who play sports $=$ Total number of students $-$ Number of students who play neither sport $\newline$ Number of students who play sports $= 29 - 11 = 18$
Find Probability: Now we have the number of students who play sports ( $18$ ), but this includes students who might play both basketball and baseball. To find the probability that a student chosen at random plays basketball or baseball, we need to divide the number of students who play sports by the total number of students. $\newline$ Probability = Number of students who play sports / Total number of students $\newline$ Probability = $\frac{18}{29}$

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