To solve for the probability that a randomly selected student with a Master's degree majored in either Business, Education, or Engineering, we need to follow these steps:
1. Identify the number of students in each major:
- Mathematics: 216
- English: 207
- Engineering: 78
- Business: 178
- Education: 227
2. Calculate the total number of students:
[tex]\[
\text{Total number of students} = 216 + 207 + 78 + 178 + 227 = 906
\][/tex]
3. Sum the frequencies of the students majoring in Business, Education, and Engineering:
[tex]\[
\text{Sum for Business, Education, and Engineering} = 178 + 227 + 78 = 483
\][/tex]
4. Calculate the probability by dividing the sum of Business, Education, and Engineering majors by the total number of students:
[tex]\[
\text{Probability} = \frac{483}{906} = 0.533
\][/tex]
5. Round the probability to three decimal places (though it is already at three decimal places in this case):
[tex]\[
\text{Probability (rounded to three decimal places)} = 0.533
\][/tex]
Given these calculations, the correct answer is:
C. 0.533
