Questions: In a certain Algebra 2 class of 29 students, 9 of them play basketball and 11 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?

In a certain Algebra 2 class of 29 students, 9 of them play basketball and 11 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?
Transcript text: In a certain Algebra 2 class of 29 students, 9 of them play basketball and 11 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?
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Solution

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Solution Steps

To find the probability that a student chosen randomly from the class plays basketball or baseball, we can use the principle of inclusion-exclusion. First, we calculate the total number of students who play either sport by adding the number of basketball players and baseball players, then subtracting those who play both sports to avoid double-counting. Finally, we divide this number by the total number of students in the class to get the probability.

Step 1: Determine the Total Number of Students Playing Either Sport

To find the total number of students who play either basketball or baseball, we use the principle of inclusion-exclusion. The formula is:

\[ \text{Either Sport} = \text{Basketball Players} + \text{Baseball Players} - \text{Both Sports} \]

Substituting the given values:

\[ \text{Either Sport} = 9 + 11 - 4 = 16 \]

Step 2: Calculate the Probability

The probability that a randomly chosen student plays either basketball or baseball is given by the ratio of the number of students who play either sport to the total number of students in the class:

\[ P(\text{Basketball or Baseball}) = \frac{\text{Either Sport}}{\text{Total Students}} = \frac{16}{29} \]

Calculating this gives:

\[ P(\text{Basketball or Baseball}) \approx 0.5517 \]

Final Answer

\(\boxed{\frac{16}{29}}\)

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