Questions: A college finds that of the 861 students taking math, 525 students are business majors and 102 students are taking math and are business majors. How many students are math or are business majors?

Solution Steps

To find the number of students who are either taking math or are business majors, we can use the principle of inclusion-exclusion. This principle states that the total number of students in either group is the sum of the students in each group minus the students who are counted twice (those who are in both groups).

1. Add the number of students taking math to the number of business majors.
2. Subtract the number of students who are both taking math and are business majors to avoid double-counting.

We are given the following values:

• Total number of students taking math: \( n(M) = 861 \)
• Total number of business majors: \( n(B) = 525 \)
• Number of students who are both taking math and are business majors: \( n(M \cap B) = 102 \)

To find the total number of students who are either taking math or are business majors, we use the formula: \[ n(M \cup B) = n(M) + n(B) - n(M \cap B) \]

Substituting the given values into the formula: \[ n(M \cup B) = 861 + 525 - 102 \]

Calculating the expression: \[ n(M \cup B) = 861 + 525 - 102 = 1284 \]

Final Answer