Please help me to solve, I got it wrong! Explain whether the following could be
ID: 3144332 • Letter: P
Question
Please help me to solve, I got it wrong!
Explain whether the following could be true: In a survey of 263 students, 153 were taking algebra, 94 were taking biology, and 16 were taking neither of the two subjects.
Choose the correct answer below and, if necessary, fill in any answer boxes to complete your choice.
A.
No this could not be true because if 16 students are taking neither of the two subjects then the distribution of students implies there will have to be more than 263 total students.
B.
Yes this could be true if there were ____students taking algebra but not biology, and there were____students taking biology but not algebra.
Explanation / Answer
NUmber of total students = 263
Algebra (A) = 153
Biology (B) = 94
Neither of two subjects (A U B )' = 16
so if Algebra and Biology are mutually exclusive set means A B = (Null Set)
Here if we assume null set thaan Total students = A + B + (A U B )' = 153 + 16 + 94 = 263
which is same as total number of students. Option B is correct as This could be true if there were 153 students taking algebra but not biology, and there were 94 students but not algebra. That means there is no mutual students who have common subjects bilogy and algebra both.