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In a certain Algebra 2 class of 29 students, 14 of them play basketball and 8 of them play baseball. There are 2 students who play both sports. 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, $14$ of them play basketball and $8$ of them play baseball. There are $2$ students who play both sports. 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,

14

of them play basketball and

8

of them play baseball. There are

2

students who play both sports. What is the probability that a student chosen randomly from the class plays basketball or baseball?

\newline

Answer:

Determine Total Number: Determine the total number of students who play either basketball or baseball. $\newline$ To find the number of students who play either basketball or baseball, we use the principle of inclusion-exclusion. $\newline$ Number of students who play basketball or baseball = Number of basketball players + Number of baseball players - Number of students who play both sports.
Calculate Students: Calculate the number of students who play either basketball or baseball. $\newline$ Number of students who play basketball or baseball = $14$ (basketball players) + $8$ (baseball players) - $2$ (students who play both). $\newline$ = $14 + 8 - 2$ $\newline$ = $20$
Calculate Probability: Calculate the probability that a student chosen randomly plays basketball or baseball. $\newline$ Probability = Number of students who play basketball or baseball / Total number of students in the class. $\newline$ Probability = $\frac{22}{29}$
Simplify Fraction: Simplify the fraction (if possible) to express the probability in simplest terms. $\newline$ The fraction $\frac{22}{29}$ cannot be simplified further as $22$ and $29$ have no common factors other than $1$ .

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