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Math  /  Data & Statistics

QuestionThere are 200 students in the 7th grade class at Brookside Middle School. Of these students, 12%12 \% play volleyball and 15%15 \% play baseball. Four students play on both teams. What is the probability that a student plays either volleyball or baseball? A. 27%27 \% B. 30%30 \% C. 22%22 \% D. 25%25 \% SUBMIT

Studdy Solution

STEP 1

1. The total number of students is 200.
2. 12%12\% of students play volleyball.
3. 15%15\% of students play baseball.
4. Four students play both volleyball and baseball.

STEP 2

1. Calculate the number of students who play volleyball.
2. Calculate the number of students who play baseball.
3. Use the principle of inclusion-exclusion to find the number of students who play either volleyball or baseball.
4. Calculate the probability that a student plays either volleyball or baseball.

STEP 3

Calculate the number of students who play volleyball:
\[ \text{Number of volleyball players} = 0.12 \times 200 = 24 $

STEP 4

Calculate the number of students who play baseball:
\[ \text{Number of baseball players} = 0.15 \times 200 = 30 $

STEP 5

Use the principle of inclusion-exclusion to find the number of students who play either volleyball or baseball:
Number of students who play either sport=24+30−4=50\text{Number of students who play either sport} = 24 + 30 - 4 = 50

STEP 6

Calculate the probability that a student plays either volleyball or baseball:
Probability=50200=0.25=25%\text{Probability} = \frac{50}{200} = 0.25 = 25\%
The probability that a student plays either volleyball or baseball is:
25% \boxed{25\%}

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