Geometry

Question Analysis
This question involves calculating the probability of mutually exclusive events within the context of course enrollment.
The main focus is on recognizing that a student cannot be enrolled in Spanish only and French only at the same time, making these two events mutually exclusive.
Then, applying the addition rule for mutually exclusive events, , to find the probability of a student taking either Spanish or French.

Key Concept Explanation
Mutually exclusive events are those that cannot happen simultaneously.
In probability, for mutually exclusive events and , the probability of the union of these events (either or occurring) is the sum of their individual probabilities.
This is because there is no overlap between the two events, so for mutually exclusive events.

Step - by - Step Solution
First, identify the number of favorable outcomes for each event and the total number of outcomes. The total number of students in the class is 30, which represents the total number of possible outcomes when selecting a student.
Calculate the probability of event (a student taking Spanish only).
There are 12 students taking Spanish only, so .
Calculate the probability of event (a student taking French only).
There are 8 students taking French only, so

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