To solve this problem, let's find the percentage of students taking either a math class, an English class, or both. We can use the Addition Rule for probabilities, which states:
[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]
Here, \( P(A \cup B) \) represents the probability (or percentage) of students taking either Math or English. \( P(A) \) is the percentage of students taking Math, \( P(B) \) is the percentage of students taking English, and \( P(A \cap B) \) is the percentage of students taking both Math and English.
Given:
- Percentage of students taking Math (\( P(A) \)): \( 80\% \)
- Percentage of students taking English (\( P(B) \)): \( 77\% \)
- Percentage of students taking both Math and English (\( P(A \cap B) \)): \( 77\% \)
We can substitute these values into the Addition Rule formula to find the percentage of students taking either Math or English:
[tex]\[ P(A \cup B) = 80\% + 77\% - 77\% \][/tex]
Perform the arithmetic:
[tex]\[ P(A \cup B) = 80\% \][/tex]
Thus, the percentage of students taking either a Math class or an English class or both is:
[tex]\[ 80\% \][/tex]
In conclusion:
- Percentage of students taking Math: \( 80\% \)
- Percentage of students taking English: \( 77\% \)
- Percentage of students taking both Math and English: \( 77\% \)
- Percentage of students taking either Math or English or both: [tex]\( 80\% \)[/tex]
