The problem is asking to find the probability that a randomly chosen student bought either an apple or a banana.

To do this, we use the following steps:

1. Total number of students (items of fruit bought): 135 students.

2. Number of students who bought apples: 36 students.

3. Number of students who bought bananas: 33 students.

4. To find the probability, we calculate the number of favorable outcomes (students who bought an apple or a banana) and divide it by the total number of outcomes (total number of students).

Thus, the probability is: $P(\text{apple or banana}) = \frac{\text{Number of students who bought apples or bananas}}{\text{Total number of students}} = \frac{36 + 33}{135} = \frac{69}{135}$

Now, simplifying the fraction: $\frac{69}{135} = \frac{23}{45}$

So, the probability is $\frac{23}{45}$.

Would you like a further explanation of how to interpret or calculate other probabilities in this scenario?

Here are some related questions to consider:

1. How would the probability change if we were asked about students who bought apples, bananas, or oranges?
2. What is the probability of a student buying a fruit other than an apple, banana, or orange?
3. If the probability of choosing a student who bought a peach is $\frac{24}{135}$, how would that compare to other fruits?
4. How do you convert the probability into a percentage?
5. If a second student is randomly chosen, how would we calculate the probability they bought a fruit similar to the first student's choice?

Tip: Always remember that the total probability of all possible outcomes must add up to 1!