The probability that the first student selected as a homeroom representative is wearing glasses or takes the bus to school is 18/25.
Here's how we can solve this:
Total number of students: There are 25 students in Maya's homeroom.
Number of students wearing glasses: 10 students wear glasses.
Number of students taking the bus: 14 students take the bus to school.
Number of students wearing glasses and taking the bus: 6 students wear glasses and take the bus.
Overlapping students: We need to be careful not to count students twice.
In this case, the number of students who wear glasses and take the bus is already included in the number of students who wear glasses and the number of students who take the bus.
Therefore, to find the total number of students who either wear glasses or take the bus, we can add the number of students in each group and then subtract the number of students who are counted twice.
Total number of students wearing glasses or taking the bus = (Number of students wearing glasses) + (Number of students taking the bus) - (Number of students wearing glasses and taking the bus)
Total number of students wearing glasses or taking the bus = 10 + 14 - 6
Total number of students wearing glasses or taking the bus = 18
Therefore, the probability that the first student selected as a homeroom representative is wearing glasses or takes the bus to school is 18 out of 25.