Geometry

Question Analysis
This question involves calculating the probability of mutually exclusive events within the context of club membership.
The main focus is on recognizing that a member cannot be in both the debate team and the drama club simultaneously, making these two events mutually exclusive, and applying the addition rule for mutually exclusive events, , to find the probability of a member being in either the debate team or the drama club.

Key Concept Explanation
Mutually exclusive events are events that cannot occur at the same time.
In probability theory, when two events and are mutually exclusive, the probability of either or happening is the sum of their individual probabilities.
This is because there is no overlap between the two events, so there is no need to subtract any intersection probability (since 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 members in the club is 25, so the total number of possible outcomes when selecting a member is 25.
Calculate the probability of event (selecting a member from the debate team). There are 10 members in the debate team, so .
Calculate the probability of event (selecting a member from the drama club). There are 8 members in the drama club, so

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