To find the probability that a student plays either volleyball or baseball, we can follow these steps:
1. Determine the number of students who play volleyball:
- There are 200 students in total.
- 12% of them play volleyball.
- Therefore, the number of students who play volleyball is [tex]\( 200 \times 0.12 = 24 \)[/tex].
2. Determine the number of students who play baseball:
- 15% of the total students play baseball.
- Therefore, the number of students who play baseball is [tex]\( 200 \times 0.15 = 30 \)[/tex].
3. Determine the number of students who play both sports:
- It is given that 4 students play both volleyball and baseball.
4. Calculate the number of students who play either volleyball or baseball:
- We use the principle of inclusion-exclusion for this calculation.
- The formula is [tex]\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)[/tex].
- Here, [tex]\( P(A) \)[/tex] is the number of students who play volleyball, [tex]\( P(B) \)[/tex] is the number who play baseball, and [tex]\( P(A \cap B) \)[/tex] is those who play both.
- Hence, [tex]\( \text{Number of students who play either volleyball or baseball} = 24 + 30 - 4 = 50 \)[/tex].
5. Determine the probability that a student plays either volleyball or baseball:
- The probability is found by dividing the number of students who play either sport by the total number of students.
- Hence, the probability is [tex]\( \frac{50}{200} \times 100 \% = 25 \% \)[/tex].
So, the probability that a student plays either volleyball or baseball is [tex]\( 25 \% \)[/tex].
The correct answer is A. [tex]\( 25 \% \)[/tex].
