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In a certain Algebra 2 class of 23 students, 9 of them play basketball and 13 of them play baseball. There are 7 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 $23$ students, $9$ of them play basketball and $13$ of them play baseball. There are $7$ 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

23

students,

9

of them play basketball and

13

of them play baseball. There are

7

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

\newline

Answer:

Find Total Students: To find the probability that a student plays basketball or baseball, we need to use the principle of inclusion-exclusion because some students play both sports.
Subtract Both Sports: First, let's find the total number of students who play at least one of the sports. We add the number of basketball players to the number of baseball players. $\newline$ Number of students playing at least one sport $=$ Number of basketball players $+$ Number of baseball players $\newline$ $= 9 + 13$ $\newline$ $= 22$ $\newline$ However, this count includes the students who play both sports twice, so we need to subtract the number of students who play both sports.
Calculate Probability: Now, we subtract the number of students who play both sports to avoid double-counting. $\newline$ Number of students playing at least one sport = $22 - \text{Number of students who play both sports}$ $\newline$ = $22 - 7$ $\newline$ = $15$
Simplify Fraction: The probability that a student chosen randomly from the class plays basketball or baseball is the number of students who play at least one sport divided by the total number of students in the class. $\newline$ Probability = Number of students playing at least one sport / Total number of students $\newline$ = $\frac{15}{23}$
Simplify Fraction: The probability that a student chosen randomly from the class plays basketball or baseball is the number of students who play at least one sport divided by the total number of students in the class. $\newline$ Probability = Number of students playing at least one sport / Total number of students $\newline$ = $\frac{15}{23}$ We simplify the fraction if possible. $\newline$ $\frac{15}{23}$ cannot be simplified further.

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