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In a certain Algebra 2 class of 22 students, 7 of them play basketball and 13 of them play baseball. There are 4 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 $22$ students, $7$ of them play basketball and $13$ of them play baseball. There are $4$ 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

22

students,

7

of them play basketball and

13

of them play baseball. There are

4

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

\newline

Answer:

Identify 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.
Calculate Students Playing 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 and then subtract the number of students who play both to avoid double-counting. $\newline$ Number of students playing at least one sport = Number of basketball players + Number of baseball players - Number of students playing both sports
Calculate Probability: Now, let's plug in the numbers: $\newline$ Number of students playing at least one sport = $7$ (basketball players) + $13$ (baseball players) - $4$ (students playing both sports) $\newline$ Number of students playing at least one sport = $7 + 13 - 4 = 16$
Simplify Fraction: The probability that a student chosen randomly plays basketball or baseball is the number of students playing at least one sport divided by the total number of students in the class. $\newline$ Probability = $\frac{\text{Number of students playing at least one sport}}{\text{Total number of students}}$
Simplify Fraction: The probability that a student chosen randomly plays basketball or baseball is the number of students playing at least one sport divided by the total number of students in the class. Probability = $\frac{\text{Number of students playing at least one sport}}{\text{Total number of students}}$ Now, let's calculate the probability: Probability = $\frac{16}{22}$
Simplify Fraction: The probability that a student chosen randomly plays basketball or baseball is the number of students playing at least one sport divided by the total number of students in the class. $\newline$ Probability = $\frac{\text{Number of students playing at least one sport}}{\text{Total number of students}}$ Now, let's calculate the probability: $\newline$ Probability = $\frac{16}{22}$ To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ Probability = $\frac{(16 / 2)}{(22 / 2)}$ $\newline$ Probability = $\frac{8}{11}$

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